Learning Poisson Binomial Distributions
Daskalakis, Constantinos; Diakonikolas, Ilias; Servedio, Rocco A
2015-01-01
We consider a basic problem in unsupervised learning: learning an unknown Poisson binomial distribution. A Poisson binomial distribution (PBD) over TeX is the distribution of a sum of TeX independent Bernoulli random variables which may have arbitrary, potentially non-equal, expectations. These distributions were first studied by Poisson (Recherches sur la Probabilitè des jugements en matié criminelle et en matiére civile. Bachelier, Paris, 1837) and are a natural TeX -parameter generalizatio...
Learning Poisson Binomial Distributions
Daskalakis, Constantinos; Servedio, R
2011-01-01
We consider a basic problem in unsupervised learning: learning an unknown \\emph{Poisson Binomial Distribution} over $\\{0,1,...,n\\}$. A Poisson Binomial Distribution (PBD) is a sum $X = X_1 + ... + X_n$ of $n$ independent Bernoulli random variables which may have arbitrary expectations. We work in a framework where the learner is given access to independent draws from the distribution and must (with high probability) output a hypothesis distribution which has total variation distance at most $\\eps$ from the unknown target PBD. As our main result we give a highly efficient algorithm which learns to $\\eps$-accuracy using $\\tilde{O}(1/\\eps^3)$ samples independent of $n$. The running time of the algorithm is \\emph{quasilinear} in the size of its input data, i.e. $\\tilde{O}(\\log(n)/\\eps^3)$ bit-operations (observe that each draw from the distribution is a $\\log(n)$-bit string). This is nearly optimal since any algorithm must use $\\Omega(1/\\eps^2)$ samples. We also give positive and negative results for some extensi...
A new Markov Binomial distribution.
Omey, Edward; Minkova, Leda D.
2011-01-01
In this paper, we introduce a two state homogeneous Markov chain and define a geometric distribution related to this Markov chain. We define also the negative binomial distribution similar to the classical case and call it NB related to interrupted Markov chain. The new binomial distribution is related to the interrupted Markov chain. Some characterization properties of the Geometric distributions are given. Recursion formulas and probability mass functions for the NB distribution and the new...
Distinguishing between Binomial, Hypergeometric and Negative Binomial Distributions
Wroughton, Jacqueline; Cole, Tarah
2013-01-01
Recognizing the differences between three discrete distributions (Binomial, Hypergeometric and Negative Binomial) can be challenging for students. We present an activity designed to help students differentiate among these distributions. In addition, we present assessment results in the form of pre- and post-tests that were designed to assess the…
A Markov-binomial distribution
Santos, J.; S. Van Gulck; OMEY, E.
2007-01-01
Let ${X_{i},igeq 1}$ denote a sequence of $left{ 0,1 ight} $%-variables and suppose that the sequence forms a {sc Markov} Chain. In the paperwe study the number of successes $S_{n}=X_{1}+X_{2}+cdots+X_{n}$ and we studythe number of experiments $Y(r)$ up to the $r$-$th$ success. In the i.i.d.case $S_{n}$ has a binomial distribution and $Y(r)$ has a negative binomialdistribution and the asymptotic behaviour is well known. In the more general{sc Markov} chain case, we prove a central limit theor...
A Characterization of the Negative Binomial Distribution
Kolev, Nikolay(Department of Physics, University of Regina, SK S4S 0A2, Canada); Minkova, Leda
2000-01-01
Only a few characterizations have been obtained in literatute for the negative binomial distribution (see Johnson et al., Chap. 5, 1992). In this article a characterization of the negative binomial distribution related to random sums is obtained which is motivated by the geometric distribution characterization given by Khalil et al. (1991). An interpretation in terms of an unreliable system is given.
The Negative Binomial Distribution in Quantum Physics
Söderholm, Jonas; Inoue, Shuichiro
2009-06-01
We give examples of situations where the negative binomial distribution has appeared in quantum physics since its debut in the work of Planck. Several of its properties are reviewed, and Mandel's Q-parameter is shown to play an interesting role. The photon-pair distributions of squeezed vacuum and squeezed single-photon states are identified as negative binomial.
On approximation of Markov binomial distributions
Xia, Aihua; 10.3150/09-BEJ194
2010-01-01
For a Markov chain $\\mathbf{X}=\\{X_i,i=1,2,...,n\\}$ with the state space $\\{0,1\\}$, the random variable $S:=\\sum_{i=1}^nX_i$ is said to follow a Markov binomial distribution. The exact distribution of $S$, denoted $\\mathcal{L}S$, is very computationally intensive for large $n$ (see Gabriel [Biometrika 46 (1959) 454--460] and Bhat and Lal [Adv. in Appl. Probab. 20 (1988) 677--680]) and this paper concerns suitable approximate distributions for $\\mathcal{L}S$ when $\\mathbf{X}$ is stationary. We conclude that the negative binomial and binomial distributions are appropriate approximations for $\\mathcal{L}S$ when $\\operatorname {Var}S$ is greater than and less than $\\mathbb{E}S$, respectively. Also, due to the unique structure of the distribution, we are able to derive explicit error estimates for these approximations.
On hypergeometric generalized negative binomial distribution
Ghitany, M. E.; Al-Awadhi, S. A.; S. L. Kalla
2002-01-01
It is shown that the hypergeometric generalized negative binomial distribution has moments of all positive orders, is overdispersed, skewed to the right, and leptokurtic. Also, a three-term recurrence relation for computing probabilities from the considered distribution is given. Application of the distribution to entomological field data is given and its goodness-of-fit is demonstrated.
On hypergeometric generalized negative binomial distribution
Directory of Open Access Journals (Sweden)
M. E. Ghitany
2002-01-01
Full Text Available It is shown that the hypergeometric generalized negative binomial distribution has moments of all positive orders, is overdispersed, skewed to the right, and leptokurtic. Also, a three-term recurrence relation for computing probabilities from the considered distribution is given. Application of the distribution to entomological field data is given and its goodness-of-fit is demonstrated.
Methods of Estimation of Generalized Negative Binomial Distribution
Kumar, Abhay; Bharti, Ramesh Chandra; Singh, Sree Kant; Mishra, Amarendra; Singh, Krishna Murari
2014-01-01
The negative binomial distribution was perhaps the first probability distribution, considered in statistics, whose variance is larger than its mean. On account of wide variety of available discrete distributions, the research workers in applied fields have begun to wonder which distribution would be most suitable one in a particular case and how to choose it. Generalized Negative Binomial Distribution (GNBD) reduces the binomial or the negative binomial distribution as particular cases and co...
Library Book Circulation and the Beta-Binomial Distribution.
Gelman, E.; Sichel, H. S.
1987-01-01
Argues that library book circulation is a binomial rather than a Poisson process, and that individual book popularities are continuous beta distributions. Three examples demonstrate the superiority of beta over negative binomial distribution, and it is suggested that a bivariate-binomial process would be helpful in predicting future book…
On approximation of Markov binomial distributions
Xia, Aihua; Zhang, Mei
2009-01-01
For a Markov chain $\\mathbf{X}=\\{X_i,i=1,2,...,n\\}$ with the state space $\\{0,1\\}$, the random variable $S:=\\sum_{i=1}^nX_i$ is said to follow a Markov binomial distribution. The exact distribution of $S$, denoted $\\mathcal{L}S$, is very computationally intensive for large $n$ (see Gabriel [Biometrika 46 (1959) 454--460] and Bhat and Lal [Adv. in Appl. Probab. 20 (1988) 677--680]) and this paper concerns suitable approximate distributions for $\\mathcal{L}S$ when $\\mathbf{X}$ is stationary. We...
Generating functions for generalized binomial distributions
Bergeron, H.; Curado, E. M. F.; Gazeau, J. P.; Rodrigues, Ligia M. C. S.
2012-10-01
In a recent article generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal probability distributions was a key point to allow to give them a statistical interpretation in terms of probabilities. In this article we present an approach based on generating functions that solves the previous difficulties. Our main theorem makes explicit the conditions under which those formal probability distributions are always non-negative. Therefore, the constraints of non-negativeness are automatically fulfilled giving a complete characterization in terms of generating functions. A large number of analytical examples becomes available.
Does the negative binomial distribution add up?
Grafen, A; Woolhouse, M E
1993-12-01
The negative binomial distribution (NBD) is widely used to describe the distribution of parasitic helminths in a number of host individuals and has proved a useful, though possibly overused, empirical and theoretical device. It is therefore important that the limits to the applicability of the NBD be clearly defined. In this paper, Alan Grafen and Mark Woolhouse consider applications of the NBD in situations where either the host or parasite population can be divided into subpopulations of different types (eg. by age, sex or genotype), and they describe the relationships between the frequency distributions relevant to the different subpopulations and those relevant to the total population. PMID:15463698
Negative Binomial and Multinomial States: probability distributions and coherent states
Fu, Hong-Chen; Sasaki, Ryu
1996-01-01
Following the relationship between probability distribution and coherent states, for example the well known Poisson distribution and the ordinary coherent states and relatively less known one of the binomial distribution and the $su(2)$ coherent states, we propose ``interpretation'' of $su(1,1)$ and $su(r,1)$ coherent states ``in terms of probability theory''. They will be called the ``negative binomial'' (``multinomial'') ``states'' which correspond to the ``negative'' binomial (multinomial)...
Negative Binomial-Lindley Distribution and Its Application
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Hossein Zamani
2010-01-01
Full Text Available Problem statement: The modeling of claims count is one of the most important topics in actuarial theory and practice. Many attempts were implemented in expanding the classes of mixed and compound distributions, especially in the distribution of exponential family, resulting in a better fit on count data. In some cases, it is proven that mixed distributions, in particular mixed Poisson and mixed negative binomial, provided better fit compared to other distributions. Approach: In this study, we introduce a new mixed negative binomial distribution by mixing the distributions of negative binomial (r,p and Lindley (θ, where the reparameterization of p = exp(-λ is considered. Results: The closed form and the factorial moment of the new distribution, i.e., the negative binomial-Lindley distribution, are derived. In addition, the parameters estimation for negative binomial-Lindley via the method of moments (MME and the Maximum Likelihood Estimation (MLE are provided. Conclusion: The application of negative binomial-Lindley distribution is carried out on two samples of insurance data. Based on the results, it is shown that the negative binomial-Lindley provides a better fit compared to the Poisson and the negative binomial for count data where the probability at zero has a large value.
Wigner Function of Density Operator for Negative Binomial Distribution
Institute of Scientific and Technical Information of China (English)
HE Min-Hua; XU Xing-Lei; ZHANG Duan-Ming; LI Hong-Qi; PAN Gui-Jun; YIN Yan-Ping; CHEN Zhi-Yuan
2008-01-01
By using the technique of integration within an ordered product (IWOP) of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator.
Convergence properties of the q-deformed binomial distribution
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Martin Zeiner
2010-03-01
Full Text Available We consider the $q$-deformed binomial distribution introduced by{sc S. C. Jing:} {it The {$q$}-deformed binomial distribution and its asymptotic behaviour,}J. Phys. A {f 27} (2 (1994, 493--499and{sc W. S. Chung} et al: {it {$q$}-deformed probability and binomial distribution,} Internat. J. Theoret. Phys.{f 34} (11 (1995, 2165--2170and establish several convergence results involvingthe Euler and the exponential distribution; some of them are $q$-analogues of classical results.
The negative binomial distribution in quark jets with fixed flavour
Alberto GiovanniniTurin U. & INFN, Turin; Sergio Lupia(Munich, Max Planck Inst.); Roberto Ugoccioni(Lund U.)
2015-01-01
We show that both the multiplicity distribution and the ratio of factorial cumulants over factorial moments for 2-jet events in e+e- annihilation at the Z^0 peak can be well reproduced by the weighted superposition of two negative binomial distributions, associated to the contribution of $b\\bar b$ and light flavoured events respectively. The negative binomial distribution is then suggested to describe the multiplicity distribution of 2-jet events with fixed flavour.
Negative Binomial Distribution and the multiplicity moments at the LHC
Praszalowicz, Michal
2011-10-01
In this work we show that the latest LHC data on multiplicity moments C2-C5 are well described by a two-step model in the form of a convolution of the Poisson distribution with energy-dependent source function. For the source function we take Γ Negative Binomial Distribution. No unexpected behavior of Negative Binomial Distribution parameter k is found. We give also predictions for the higher energies of 10 and 14 TeV.
Negative Binomial Distribution and the multiplicity moments at the LHC
Praszalowicz, Michal
2011-01-01
In this work we show that the latest LHC data on multiplicity moments $C_2-C_5$ are well described by a two-step model in the form of a convolution of the Poisson distribution with energy-dependent source function. For the source function we take $\\Gamma$ Negative Binomial Distribution. No unexpected behavior of Negative Binomial Distribution parameter $k$ is found. We give also predictions for the higher energies of 10 and 14 TeV.
Self-Similarity of the Negative Binomial Multiplicity Distributions
Calucci, Giorgio; Treleani, Daniele
1997-01-01
The negative binomial distribution is self similar: If the spectrum over the whole rapidity range gives rise to a negative binomial, in absence of correlation and if the source is unique, also a partial range in rapidity gives rise to the same distribution. The property is not seen in experimental data, which are rather consistent with the presence of a number of independent sources. When multiplicities are very large self similarity might be used to isolate individual sources is a complex pr...
Estimation of Log-Linear-Binomial Distribution with Applications
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Elsayed Ali Habib
2010-01-01
Full Text Available Log-linear-binomial distribution was introduced for describing the behavior of the sum of dependent Bernoulli random variables. The distribution is a generalization of binomial distribution that allows construction of a broad class of distributions. In this paper, we consider the problem of estimating the two parameters of log-linearbinomial distribution by moment and maximum likelihood methods. The distribution is used to fit genetic data and to obtain the sampling distribution of the sign test under dependence among trials.
On intervened negative binomial distribution and some of its properties
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C. Satheesh Kumar
2013-05-01
Full Text Available Here we develop a new class of discrete distribution namely intervened negative binomial distribution and derive its probability generating function, mean, variance and an expression for its factorial moments. Estimation of the parameters of the distribution is described and the distribution has been fitted to a well known data set.
On intervened negative binomial distribution and some of its properties
Satheesh Kumar, C.; S. Sreejakumari
2013-01-01
Here we develop a new class of discrete distribution namely intervened negative binomial distribution and derive its probability generating function, mean, variance and an expression for its factorial moments. Estimation of the parameters of the distribution is described and the distribution has been fitted to a well known data set.
Hadronic multiplicity distributions: the negative binomial and its alternatives
International Nuclear Information System (INIS)
We review properties of the negative binomial distribution, along with its many possible statistical or dynamical origins. Considering the relation of the multiplicity distribution to the density matrix for boson systems, we re-introduce the partially coherent laser distribution, which allows for coherent as well as incoherent hadronic emission from the k fundamental cells, and provides equally good phenomenological fits to existing data. The broadening of non-single diffractive hadron-hadron distributions can be equally well due to the decrease of coherence with increasing energy as to the large (and rapidly decreasing) values of k deduced from negative binomial fits. Similarly the narrowness of e+-e- multiplicity distribution is due to nearly coherent (therefore nearly Poissonian) emission from a small number of jets, in contrast to the negative binomial with enormous values of k. 31 refs
A continuous version of the negative binomial distribution
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Nimai Kumar Chandra
2013-05-01
Full Text Available While discretization of continuous distributions have been attempted for many life distributions the reverse has hardly been attempted. The present endeavor is to establish a reverse relationship by offering a continuous counter part of a discrete distribution namely negative binomial distribution. Different properties of this distribution have been established for a special choice of the parametric value covering class properties, ordering and mean residual life.
A continuous version of the negative binomial distribution
Nimai Kumar Chandra; Dilip Roy
2013-01-01
While discretization of continuous distributions have been attempted for many life distributions the reverse has hardly been attempted. The present endeavor is to establish a reverse relationship by offering a continuous counter part of a discrete distribution namely negative binomial distribution. Different properties of this distribution have been established for a special choice of the parametric value covering class properties, ordering and mean residual life.
Negative Binomial-Lindley Distribution and Its Application
Hossein Zamani; Noriszura Ismail
2010-01-01
Problem statement: The modeling of claims count is one of the most important topics in actuarial theory and practice. Many attempts were implemented in expanding the classes of mixed and compound distributions, especially in the distribution of exponential family, resulting in a better fit on count data. In some cases, it is proven that mixed distributions, in particular mixed Poisson and mixed negative binomial, provided better fit compared to other distributions. Approach: In this study, we...
Correlation Structures of Correlated Binomial Models and Implied Default Distribution
Mori, S.; K. Kitsukawa; M. Hisakado
2006-01-01
We show how to analyze and interpret the correlation structures, the conditional expectation values and correlation coefficients of exchangeable Bernoulli random variables. We study implied default distributions for the iTraxx-CJ tranches and some popular probabilistic models, including the Gaussian copula model, Beta binomial distribution model and long-range Ising model. We interpret the differences in their profiles in terms of the correlation structures. The implied default distribution h...
Tchikilev, O. G.
1997-01-01
It is shown that simple extension of the modified negative binomial distribution describes negatively charged particle multiplicity distributions in e+e- annihilation, measured in the whole phase space, as well as the modified negative binomial.
Statistical Inference for a Class of Multivariate Negative Binomial Distributions
DEFF Research Database (Denmark)
Rubak, Ege H.; Møller, Jesper; McCullagh, Peter
This paper considers statistical inference procedures for a class of models for positively correlated count variables called -permanental random fields, and which can be viewed as a family of multivariate negative binomial distributions. Their appealing probabilistic properties have earlier been...... studied in the literature, while this is the first statistical paper on -permanental random fields. The focus is on maximum likelihood estimation, maximum quasi-likelihood estimation and on maximum composite likelihood estimation based on uni- and bivariate distributions. Furthermore, new results for...
Negative Binomial Distribution and the multiplicity moments at the LHC
Praszalowicz, Michal
2011-01-01
In this work we show that the latest LHC data on multiplicity moments $C_2-C_5$ are well described by a two-step model in the form of a convolution of the Poisson distribution with energy-dependent source function. For the source function we take $\\Gamma$ Negative Binomial Distribution. We give also predictions for the higher energies of 10 and 14 TeV.
Mixed Negative Binomial Distribution by Weighted Gamma Mixing Distribution
Stoynov, Pavel
2011-01-01
Павел Т. Стойнов - В тази работа се разглежда отрицателно биномното разпределение, известно още като разпределение на Пойа. Предполагаме, че смесващото разпределение е претеглено гама разпределение. Изведени са вероятностите в някои частни случаи. Дадени са рекурентните формули на Панжер. In this paper the mixed negative binomial distribution, known also as P´olya distribution is considered. We suppose that the mixing distribution is a weighted Gamma distribution. We derive the probabil...
KNO scaling function of modified negative binomial distribution
Nakajima, N; Biyajima, M.; Suzuki, N.
1996-01-01
We investigate the KNO scaling function of the modified negative binomial distribution (MNBD), because this MNBD can explain the oscillating behaviors of the cumulant moment observed in $e^+e^-$ annihilations and in hadronic collisions. By using a straightforward method and the Poisson transform we derive the KNO scaling function from the MNBD. The KNO form of experimental data in $e^{+}e^{-}$ collisions and hadronic collisions are analyzed by the KNO scaling function of the MNBD and that of ...
KNO scaling function of modified negative binomial distribution
Nakajima, Noriaki; Biyajima, Minoru; Suzuki, Naomichi
1997-01-01
We investigate the KNO scaling function of the modified negative binomial distribution (MNBD), because this MNBD can explain the oscillating behaviors of the cumulant moment observed in ez e{ annihilations and in hadronic collisions. By using a straightforward method and the Poisson transform we derive the KNO scaling function from the MNBD. The KNO form of experimental data in ez e{ collisions and hadronic collisions are analyzed by the KNO scaling function of the MNBD and that of the nega...
International Nuclear Information System (INIS)
The multiplicity distributions of charged hadrons produced in the deep inelastic muon-proton scattering at 280 GeV are analysed in various rapidity intervals, as a function of the total hadronic centre of mass energy W ranging from 4-20 GeV. Multiplicity distributions for the backward and forward hemispheres are also analysed separately. The data can be well parameterized by binomial distributions, extending their range of applicability to the case of lepton-proton scattering. The energy and the rapidity dependence of the parameters is presented and a smooth transition from the binomial distribution via Poissonian to the ordinary binomial is observed. (orig.)
Statistical inference for a class of multivariate negative binomial distributions
DEFF Research Database (Denmark)
Rubak, Ege Holger; Møller, Jesper; McCullagh, Peter
This paper considers statistical inference procedures for a class of models for positively correlated count variables called α-permanental random fields, and which can be viewed as a family of multivariate negative binomial distributions. Their appealing probabilistic properties have earlier been...... studied in the literature, while this is the first statistical paper on α-permanental randomfields. The focus is on maximum likelihood estimation, maximum quasi-likelihood estimation and on maximum composite likelihood estimation based on uni- and bivariate distributions. Furthermore, new results for α...
The Parameterized Complexity Analysis of Partition Sort for Negative Binomial Distribution Inputs
Singh, Niraj Kumar; Chakraborty, Soubhik
2012-01-01
The present paper makes a study on Partition sort algorithm for negative binomial inputs. Comparing the results with those for binomial inputs in our previous work, we find that this algorithm is sensitive to parameters of both distributions. But the main effects as well as the interaction effects involving these parameters and the input size are more significant for negative binomial case.
Multiplicities in Ultrarelativistic - Collisions and Negative Binomial Distribution FITS
Prorok, Dariusz
Likelihood ratio tests are performed for the hypothesis that charged-particle multiplicities measured in proton-(anti)proton collisions at √ {s} = 0.9 and 2.36 TeV are distributed according to the negative binomial form. Results indicate that the hypothesis should be rejected in the all cases of ALICE-LHC measurements in the limited pseudorapidity windows, whereas should be accepted in the corresponding cases of UA5 data. Possible explanations of that and of the disagreement with the least-squares fitting method are given.
On Size-Biased Negative Binomial Distribution and its Use in Zero-Truncated Cases
Mir, Khurshid Ahmad
2009-01-01
A size-biased negative binomial distribution, a particular case of the weighted negative binomial distribution, taking the weights as the variate values has been defined. A Bayes' estimator of size-biased negative binomial distribution (SBNBD) has been obtained by using non-informative and gamma prior distributions. Also comparison has been made of this estimator with the corresponding maximum likelihood estimator (MLE) with the help of R- Software.
Moody's Correlated Binomial Default Distributions for Inhomogeneous Portfolios
Mori, S; Kitsukawa, K
2006-01-01
This paper generalizes Moody's correlated binomial default distribution for homogeneous credit portfolio, which is introduced by Witt, to the case of inhomogeneous portfolios. As inhomogeneous portfolios, we consider two cases. In the first case, we treat a portfolio whose assets have uniform default correlation and non-uniform default probabilities. We obtain the default probability distribution and study the effect of the inhomogeneity on it. The second case corresponds to a portfolio with inhomogeneous default correlation. Assets are categorized in several different sectors and the inter-sector and intra-sector correlations are not the same. We construct the joint default probabilities and obtain the default probability distribution. We show that as the number of assets in each sector decreases, inter-sector correlation becomes more important than the intra-sector one. We study the maximum values of the inter-sector default correlation. In the modeling of portfolio credit risk, it is possible to incorporat...
The zero inflated negative binomial – Crack distribution: some properties and parameter estimation
Pornpop Saengthong; Winai Bodhisuwan; Ampai Thongteeraparp
2015-01-01
The zero inflated negative binomial-Crack (ZINB-CR) distribution is a mixture of Bernoulli distribution and negative binomial-Crack (NB-CR) distribution, which is an alternative distribution for the excessive zero counts and overdispersion. In this paper, some properties of the ZINB-CR distribution are discussed. Statistical inference of the parameters is derived by maximum likelihood estimation (MLE) and the method of moments (MM). Monte Carlo Simulations are used to evaluate the ...
Binomial Distribution Sample Confidence Intervals Estimation 5. Odds Ratio
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Sorana BOLBOACĂ
2004-02-01
Full Text Available Evaluation of the strength of association between predisposing or causal factors and disease can be express as odds ratio in case-control studies. In order to interpret correctly a point estimation of odds ratio we need to look also to its confidence intervals quality. The aim of this paper is to introduce three new methods of computing the confidence intervals, R2AC, R2Binomial, and R2BinomialC, and compare the performances with the asymptotic method called R2Wald.In order to assess the methods a PHP program was develop. First, the upper and lower confidence boundaries for all implemented methods were computes and graphically represented. Second, the experimental errors, standard deviations of the experimental errors and deviation relative to the imposed significance level α = 5% were assessed. Estimating the experimental errors and standard deviations at central point for given sample sizes was the third criterion. The R2Wald and R2AC methods were assessed using random binomial variables (X, Y and sample sizes (m, n from 4 to 1000. The methods based on the original method Binomial adjusted for odds ratio (R2Binomial, R2BinomialC functions obtain systematically the lowest deviation of the experimental errors percent relative to the expected error percent and the R2AC method, the closest average of the experimental errors percent to the expected error percent.
Ross, Nathan
2013-01-01
For a family of linear preferential attachment graphs, we provide rates of convergence for the total variation distance between the degree of a randomly chosen vertex and an appropriate power law distribution as the number of vertices tends to infinity. Our proof uses a new formulation of Stein's method for the negative binomial distribution, which stems from a distributional transformation that has the negative binomial distributions as the only fixed points.
The zero inflated negative binomial – Crack distribution: some properties and parameter estimation
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Pornpop Saengthong
2015-12-01
Full Text Available The zero inflated negative binomial-Crack (ZINB-CR distribution is a mixture of Bernoulli distribution and negative binomial-Crack (NB-CR distribution, which is an alternative distribution for the excessive zero counts and overdispersion. In this paper, some properties of the ZINB-CR distribution are discussed. Statistical inference of the parameters is derived by maximum likelihood estimation (MLE and the method of moments (MM. Monte Carlo Simulations are used to evaluate the performance of parameter estimation methods in term of mean squared error (MSE. An application of the distribution is carried out on a sample of excess zero-count data. Simulation results show that the MLE method outperforms the MM method in specific parameter values. Furthermore, the ZINB-CR provides a better fit compared to the zero inflated Poisson (ZIP, the zero inflated negative binomial (ZINB and the negative binomial-Crack (NB-CR distributions.
Chromosome aberration analysis based on a beta-binomial distribution
International Nuclear Information System (INIS)
Analyses carried out here generalized on earlier studies of chromosomal aberrations in the populations of Hiroshima and Nagasaki, by allowing extra-binomial variation in aberrant cell counts corresponding to within-subject correlations in cell aberrations. Strong within-subject correlations were detected with corresponding standard errors for the average number of aberrant cells that were often substantially larger than was previously assumed. The extra-binomial variation is accomodated in the analysis in the present report, as described in the section on dose-response models, by using a beta-binomial (B-B) variance structure. It is emphasized that we have generally satisfactory agreement between the observed and the B-B fitted frequencies by city-dose category. The chromosomal aberration data considered here are not extensive enough to allow a precise discrimination between competing dose-response models. A quadratic gamma ray and linear neutron model, however, most closely fits the chromosome data. (author)
Analysis of generalized negative binomial distributions attached to hyperbolic Landau levels
Chhaiba, Hassan; Demni, Nizar; Mouayn, Zouhair
2016-01-01
To each hyperbolic Landau level of the Poincar\\'e disc is attached a generalized negative binomial distribution. In this paper, we compute the moment generating function of this distribution and supply its decomposition as a perturbation of the negative binomial distribution by a finitely-supported measure. Using the Mandel parameter, we also discuss the nonclassical nature of the associated coherent states. Next, we determine the L\\'evy-Kintchine decomposition its characteristic function whe...
Bacterial Density in Water Determined by Poisson or Negative Binomial Distributions
El-Shaarawi, A. H.; Esterby, S. R.; Dutka, B. J.
1981-01-01
The question of how to characterize the bacterial density in a body of water when data are available as counts from a number of small-volume samples was examined for cases where either the Poisson or negative binomial probability distributions could be used to describe the bacteriological data. The suitability of the Poisson distribution when replicate analyses were performed under carefully controlled conditions and of the negative binomial distribution for samples collected from different l...
Adil Rashid; Tariq .R. Jan
2013-01-01
In this paper, we provide a chronological overview of the recent developments in thecompounding of distributions. An attempt has been made to obtain a compound of zero truncatedgeneralized negative binomial distribution (Ztgnbd) with that of Generalized Beta Distribution(GBD). Factorial and ordinary crude moments of some zero truncated compound distributionshave also been discussed. The compound is then specialized by varying the value of β in((Ztgnbd)).
Directory of Open Access Journals (Sweden)
Adil Rashid
2013-01-01
Full Text Available In this paper, we provide a chronological overview of the recent developments in thecompounding of distributions. An attempt has been made to obtain a compound of zero truncatedgeneralized negative binomial distribution (Ztgnbd with that of Generalized Beta Distribution(GBD. Factorial and ordinary crude moments of some zero truncated compound distributionshave also been discussed. The compound is then specialized by varying the value of β in((Ztgnbd.
Characterizations of the Extended Geometric, Harris, Negative Binomial and Gamma Distributions
Sandhya, E.; Sherly, S; Jos, M K; N. Raju
2005-01-01
Extended geometric distribution is defined and its mixture is characterized by the property of having completely monotone probability sequence. Also, convolution equations and probability generating functions are used to characterize extended geometric distributions. Further, some characterizations of Harris and negative binomial distributions based on probability generating functions are obtained. Relations between these distributions are derived and finally a gamma distribution is character...
OSADA, T; Nakajima, N; Biyajima, M.; Suzuki, N.
1998-01-01
We analyze various data of multiplicity distributions by means of the Modified Negative Binomial Distribution (MNBD) and its KNO scaling function, since this MNBD explains the oscillating behavior of the cumulant moment observed in e^+e^- annihilations, h-h collisions and e-p collisions. In the present analyses, we find that the MNBD(discrete distributions) describes the data of charged particles in e^+e^- annihilations much better than the Negative Binomial Distribution (NBD). To investigate...
Analysis of generalized negative binomial distributions attached to hyperbolic Landau levels
Chhaiba, Hassan; Demni, Nizar; Mouayn, Zouhair
2016-07-01
To each hyperbolic Landau level of the Poincaré disc is attached a generalized negative binomial distribution. In this paper, we compute the moment generating function of this distribution and supply its atomic decomposition as a perturbation of the negative binomial distribution by a finitely supported measure. Using the Mandel parameter, we also discuss the nonclassical nature of the associated coherent states. Next, we derive a Lévy-Khintchine-type representation of its characteristic function when the latter does not vanish and deduce that it is quasi-infinitely divisible except for the lowest hyperbolic Landau level corresponding to the negative binomial distribution. By considering the total variation of the obtained quasi-Lévy measure, we introduce a new infinitely divisible distribution for which we derive the characteristic function.
Zhao, Zhiwen
Our purpose is to deal with the parameter estimation and hypothesis testing on the equality of two negative binomial distribution populations with missing data. The consistency and asymptotic normality of the estimations are proved. In addition statistic on testing equality of two negative distributions and its limiting distribution are obtained.
Tchikilev, O. G.
1996-01-01
It is shown that charged hadron multiplicity distributions in lepton-nucleon scattering are fairly well described by the modified negative binomial distribution in the energy range from 3-4 to 220 GeV. The energy behaviour of the parameter k is similar to the dependence observed for e+e- annihilation.
Sums of Possibly Associated Bernoulli Variables: The Conway–Maxwell-Binomial Distribution
Joseph B. Kadane
2016-01-01
The study of sums of possibly associated Bernoulli random variables has been hampered by an asymmetry between positive correlation and negative correlation. The Conway-Maxwell Binomial (COMB) distribution and its multivariate extension, the Conway-Maxwell Multinomial (COMM) distribution, gracefully model both positive and negative association. Sufficient statistics and a family of proper conjugate distributions are found. The relationship of this distribution to the exchangeable special case ...
A generalized negative binomial distribution based on an extended Poisson process
Salasar, Luis Ernesto Bueno; Leite, José Galvão; Neto, Francisco Louzada
2010-01-01
In this article we propose a generalized negative binomial distribution, which is constructed based on an extended Poisson process (a generalization of the homogeneous Poisson process). This distribution is intended to model discrete data with presence of zero-inflation and over-dispersion. For a dataset on animal abundance which presents over-dispersion and a high frequency of zeros, a comparison between our extended distribution and other common distributions used for modeling this kind of ...
Multiplicity Distributions in Strong Interactions: A Generalized Negative Binomial Model
Hegyi, S.
1996-01-01
A three-parameter discrete distribution is developed to describe the multiplicity distributions observed in total- and limited phase space volumes in different collision processes. The probability law is obtained by the Poisson transform of the KNO scaling function derived in Polyakov's similarity hypothesis for strong interactions as well as in perturbative QCD. Various characteristics of the newly proposed distribution are investigated e.g. its generating function, factorial moments, factor...
Multiplicity Distributions in Strong Interactions A Generalized Negative Binomial Model
Hegyi, S
1996-01-01
A three-parameter discrete distribution is developed to describe the multiplicity distributions observed in total- and limited phase space volumes in different collision processes. The probability law is obtained by the Poisson transform of the KNO scaling function derived in Polyakov's similarity hypothesis for strong interactions as well as in perturbative QCD. Various characteristics of the newly proposed distribution are investigated e.g. its generating function, factorial moments, factorial cumulants. Several limiting and special cases are discussed. A comparison is made to the multiplicity data available in e+e- annihilations at the Z0 peak.
The Negative Binomial Distribution as a Renewal Model for the Recurrence of Large Earthquakes
Tejedor, Alejandro; Gómez, Javier B.; Pacheco, Amalio F.
2015-01-01
The negative binomial distribution is presented as the waiting time distribution of a cyclic Markov model. This cycle simulates the seismic cycle in a fault. As an example, this model, which can describe recurrences with aperiodicities between 0 and 0.5, is used to fit the Parkfield, California earthquake series in the San Andreas Fault. The performance of the model in the forecasting is expressed in terms of error diagrams and compared with other recurrence models from literature.
Sorana BOLBOACĂ; Lorentz JÄNTSCHI
2005-01-01
Likelihood Ratio medical key parameters calculated on categorical results from diagnostic tests are usually express accompanied with their confidence intervals, computed using the normal distribution approximation of binomial distribution. The approximation creates known anomalies, especially for limit cases. In order to improve the quality of estimation, four new methods (called here RPAC, RPAC0, RPAC1, and RPAC2) were developed and compared with the classical method (called h...
Studying the Binomial Distribution Using LabVIEW
George, Danielle J.; Hammer, Nathan I.
2015-01-01
This undergraduate physical chemistry laboratory exercise introduces students to the study of probability distributions both experimentally and using computer simulations. Students perform the classic coin toss experiment individually and then pool all of their data together to study the effect of experimental sample size on the binomial…
Bo, Yizhou; Shifa, Naima
2013-09-01
An estimator for finding the abundance of a rare, clustered and mobile population has been introduced. This model is based on adaptive cluster sampling (ACS) to identify the location of the population and negative binomial distribution to estimate the total in each site. To identify the location of the population we consider both sampling with replacement (WR) and sampling without replacement (WOR). Some mathematical properties of the model are also developed.
SERVICE LEVEL ANALYSIS OF (S - 1, S) INVENTORY POLICY FOR NEGATIVE BINOMIAL DISTRIBUTED FAILURES
SUNEUNG AHN; WOOHYUN KIM
2008-01-01
This paper deals with the analysis of uncertain parameters in the (S - 1, S) inventory control policy. In order to determine the number of spare parts under the policy, parameters in a probability model for the number of failures during a replenishment lead time should be interpreted first. In case of the negative binomial distributed failures, the presented interpretation facilitates the incorporation of experts' opinions into the estimation of uncertain parameters. Determination of paramete...
Two Different Definitions of Negative Binomial Distributions%负二项分布的两个不同定义
Institute of Scientific and Technical Information of China (English)
康殿统
2014-01-01
给出了负二项分布的两个不同定义，给出了两类负二项随机变量的期望、方差与矩母函数。从直观上对这两类负二项随机变量做了描述。%Two definitions of the nega tive binomial distributions are introduced. The expectations, variances and moment generating functions for two types of the negative binomial random variables are computed. Intuitive and descriptive explanations are made for the negative binomial random variables.
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MAURICIO SADINLE
Full Text Available The negative binomial distribution is associated to the series obtained by taking derivatives of the logarithmic series. Conversely, the logarithmic series distribution is associated to the series found by integrating the series associated to the negative binomial distribution. The parameter of the number of failures of the negative binomial distribution is the number of derivatives needed to obtain the negative binomial series from the logarithmic series. The reasoning in this article could be used as an alternative method to prove that the probability mass function of the negative binomial distribution sums to one. Finally, an interpretation of the logarithmic series distribution is given by using the presented reasoning.La distribución binomial negativa está asociada a la serie obtenida de derivar la serie logarítmica. Recíprocamente, la distribución logarítmica está asociada a la serie obtenida de integrar la serie asociada a la distribución binomial negativa. El parámetro del número de fallas de la distribución binomial negativa es el número de derivadas necesarias para obtener la serie binomial negativa de la serie logarítmica. El razonamiento presentado puede emplearse como un método alternativo para probar que la función de masa de probabilidad de la distribución binomial negativa suma uno. Finalmente, se presenta una interpretación de la distribución logarítmica usando el razonamiento planteado.
Prorok, Dariusz
2011-01-01
Likelihood ratio tests are performed for the hypothesis that charged-particle multiplicities measured in proton-(anti)proton collisions at $\\sqrt{s}$ = 0.9 and 2.36 TeV are distributed according to the negative binomial form. Results indicate that the hypothesis should be rejected in the all cases of ALICE-LHC measurements in the limited pseudo-rapidity windows, whereas should be accepted in the corresponding cases of UA5 data. Possible explanations of that and of the disagreement with the le...
Prorok, Dariusz
2011-01-01
Likelihood ratio tests are performed for the hypothesis that charged-particle multiplicities measured in proton-(anti)proton collisions at $\\sqrt{s}$ = 0.9, 2.36 TeV are distributed according to the negative binomial form. Results indicate that the hypothesis should be rejected in the all cases of LHC measurements in the limited pseudo-rapidity windows, whereas should be accepted in the corresponding cases of UA5 data. Possible explanations of that and of the disagreement with the least-squares fitting method are given.
A comparison of LMC and SDL complexity measures on binomial distributions
Piqueira, José Roberto C.
2016-02-01
The concept of complexity has been widely discussed in the last forty years, with a lot of thinking contributions coming from all areas of the human knowledge, including Philosophy, Linguistics, History, Biology, Physics, Chemistry and many others, with mathematicians trying to give a rigorous view of it. In this sense, thermodynamics meets information theory and, by using the entropy definition, López-Ruiz, Mancini and Calbet proposed a definition for complexity that is referred as LMC measure. Shiner, Davison and Landsberg, by slightly changing the LMC definition, proposed the SDL measure and the both, LMC and SDL, are satisfactory to measure complexity for a lot of problems. Here, SDL and LMC measures are applied to the case of a binomial probability distribution, trying to clarify how the length of the data set implies complexity and how the success probability of the repeated trials determines how complex the whole set is.
Energy dependence of parameters of negative-binomial distributions in NN collisions
International Nuclear Information System (INIS)
We have discussed the energy dependence of the parameters left-angle n right-angle and K of the negative-binomial distributions for the full phase-space charged-particle multiplicity distributions in pp/p bar p collisions. It was shown that, under the assumption that multiparticle production is a stationary branching process, there exists a relation between the two parameters left-angle n right-angle and K. A similar relation can also be derived empirically, from information-theoretic entropy considerations. The energy dependence of one parameter then automatically determines the energy dependence of the other. It was then argued from entropy considerations that there should be an upper bound for left-angle n right-angle or conversely a lower bound for K as a function of energy. New parametrizations for the energy dependence of K were given, taking into account that K should have a lower bound, which together with the relation between the parameters left-angle n right-angle and K predicts that the average number of particles cannot be increased indefinitely with increasing c.m. system energy
Analysis of DAR(1)/D/s Queue with Quasi-Negative Binomial-II as Marginal Distribution
Kanichukattu Korakutty Jose; Bindu Abraham
2011-01-01
In this paper we consider the arrival process of a multiserver queue governed by a discrete autoregressive process of order 1 [DAR(1)] with Quasi-Negative Binomial Distribution-II as the marginal distribution. This discrete time multiserver queueing system with autoregressive arrivals is more suitable for modeling the Asynchronous Transfer Mode(ATM) multiplexer queue with Variable Bit Rate (VBR) coded teleconference traffic. DAR(1) is described by a few parameters and it is easy to match the ...
Design and analysis of three-arm trials with negative binomially distributed endpoints.
Mütze, Tobias; Munk, Axel; Friede, Tim
2016-02-20
A three-arm clinical trial design with an experimental treatment, an active control, and a placebo control, commonly referred to as the gold standard design, enables testing of non-inferiority or superiority of the experimental treatment compared with the active control. In this paper, we propose methods for designing and analyzing three-arm trials with negative binomially distributed endpoints. In particular, we develop a Wald-type test with a restricted maximum-likelihood variance estimator for testing non-inferiority or superiority. For this test, sample size and power formulas as well as optimal sample size allocations will be derived. The performance of the proposed test will be assessed in an extensive simulation study with regard to type I error rate, power, sample size, and sample size allocation. For the purpose of comparison, Wald-type statistics with a sample variance estimator and an unrestricted maximum-likelihood estimator are included in the simulation study. We found that the proposed Wald-type test with a restricted variance estimator performed well across the considered scenarios and is therefore recommended for application in clinical trials. The methods proposed are motivated and illustrated by a recent clinical trial in multiple sclerosis. The R package ThreeArmedTrials, which implements the methods discussed in this paper, is available on CRAN. PMID:26388314
Aban, Inmaculada B.; CUTTER, GARY R.; Mavinga, Nsoki
2008-01-01
In comparing the mean count of two independent samples, some practitioners would use the t-test or the Wilcoxon rank sum test while others may use methods based on a Poisson model. It is not uncommon to encounter count data that exhibit overdispersion where the Poisson model is no longer appropriate. This paper deals with methods for overdispersed data using the negative binomial distribution resulting from a Poisson-Gamma mixture. We investigate the small sample properties of the likelihood-...
On the multiplicity distribution in statistical model: (I) negative binomial distribution
Xu, Hao-jie
2016-01-01
With the distribution of principal thermodynamic variables (e.g.,volume) and the probability condition from reference multiplicity, we develop an improved baseline measure for multiplicity distribution in statistical model to replace the traditional Poisson expectations. We demonstrate the mismatches between experimental measurements and previous theoretical calculations on multiplicity distributions. We derive a general expression for multiplicity distribution, i.e. a conditional probability distribution, in statistical model and calculate its cumulants under Poisson approximation in connection with recent data for multiplicity fluctuations. We find that probability condition from reference multiplicity are crucial to explain the centrality resolution effect in experiment. With the improved baseline measure for multiplicity distribution, we can quantitatively reproduce the cumulants (cumulant products) for multiplicity distribution of total (net) charges measured in experiments.
Informative prior distributions for a binomial model to predict professional tennis results
Colin, Pierre; Bechler, Aurélien
2015-01-01
Tennis is a sport, as many others, that appears to be quite simple in the type of results (victory of one of the two players) but rather quite complex in factors that leads to this binary outcome. The perpetual evolution and increase of the way to collect data leads to more and more accurate available information about professional tennis matches. We studied the predictive properties of the binomial model representing the victory of one player against the other. Bayesian framework enables the...
Compound Negative Binomial Distribution and Compound Poisson Distribution%复合负二项分布与复合泊松分布
Institute of Scientific and Technical Information of China (English)
魏瑛源
2014-01-01
运用矩母函数证明了任何一个复合负二项分布可以写成一个复合泊松分布，并给出一个具体实例。%By using the moment generating function , we prove that a compound negative binomial distribution can be expressed as a compound Poisson distribution .An example is shown .
Ajinenko, I. V.; Belokopytov, Yu. A.; Bialkowska, H.; Boettcher, H.; Botterweck, F.; Charlet, M.; Chliapnikov, P. V.; Crijns, F.; de Roeck, A.; de Wolf, D. A.; Dziunikowska, K.; Endler, A. M. F.; Eskreys, A.; Garutchava, Z. C.; Golubkov, Y. A.; Gulkanyan, G. R.; van Hal, P.; Hakobyan, R. Sh.; Haupt, T.; Kittel, W.; Kisielewska, D.; Levchenko, B. B.; Machowski, B.; Meijers, F.; Michałowska, A. B.; Nikolaenko, V. I.; Olkiewicz, K.; Pöllänen, R.; Ronjin, V. M.; Rybin, A. M.; Saarikko, H. M. T.; Scholten, L.; Smirnova, L. N.; Tchikilev, O. G.; Uvarov, V. A.; Verbeure, F.; Wischnewski, R.
1990-12-01
The negative binomial distribution (NBD) is fitted to all charged and to negative particle multiplicity distributions in restricted rapidity intervals, both in the forward and backward c.m. hemispheres of positive meson interactions on Al and Au nuclei. For negative particle multiplicity distributions, the NBD parameters are also determined as a function of n g, the number of grey tracks, corresponding to varying number of intranuclear collisions. The data are interpreted in terms of the clan picture of Giovannini and Van Hove and compared to the MCMHA and Fritiof models. Both models reproduce quite well the global multiplicity distributions, but not when sub-samples are considered with fixed number of grey tracks. Regularities are better visible on the parton than on the particle level.
Binomial Distribution Sample Confidence Intervals Estimation 8. Number Needed to Treat/Harm
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Sorana BOLBOACĂ
2004-08-01
Full Text Available Nowadays, the number needed to treat became the most important parameter in reporting the treatment effects in clinical trials, from binary outcomes such as “positive” or “negative”. Defined as a reciprocal of the absolute risk reduction, the number needed to treat is the number of patients who need to be treated to prevent one additional adverse even. In medical literature, the number needed to treat is reported usually with its asymptotic confidence intervals, method that is used by the most software packages even if it is knows that is not the best method. The aim of this paper is to introduce three new methods of computing confidence intervals for number needed to treat/harm.Using PHP programming language was implementing the proposed methods and the asymptotic one (called here IADWald. The performance of each method, for different sample sizes (m, n and different values of binomial variables (X, Y were asses using a set of criterions: the upper and lower boundaries; the average and standard deviation of the experimental errors; the deviation of the experimental errors relative to imposed significance level (α = 5%. The methods were assess on random binomial variables X, Y (where X < m, Y < n and random sample sizes m, n (4 ≤ m, n ≤ 1000.The performances of the implemented methods of computing confidence intervals for number needed to treat/harm are present in order to be taking into consideration when a confidence interval for number needed to treat is used.
Modeling citrus huanglongbing data using a zero-inflated negative binomial distribution
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Eudmar Paiva de Almeida
2016-06-01
Full Text Available Zero-inflated data from field experiments can be problematic, as these data require the use of specific statistical models during the analysis process. This study utilized the zero-inflated negative binomial (ZINB model with the log- and logistic-link functions to describe the incidence of plants with Huanglongbing (HLB, caused by Candidatus liberibacter spp. in commercial citrus orchards in the Northwestern Parana State, Brazil. Each orchard was evaluated at different times. The ZINB model with random effects in both link functions provided the best fit, as the inclusion of these effects accounted for variations between orchards and the numbers of diseased plants. The results of this model show that older plants exhibit a lower probability of acquiring HLB. The application of insecticides on a calendar basis or during new foliage flushes resulted in a three times larger probability of developing HLB compared with applying insecticides only when the vector was detected.
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Andrei ACHIMAŞ CADARIU
2004-08-01
Full Text Available Assessments of a controlled clinical trial suppose to interpret some key parameters as the controlled event rate, experimental event date, relative risk, absolute risk reduction, relative risk reduction, number needed to treat when the effect of the treatment are dichotomous variables. Defined as the difference in the event rate between treatment and control groups, the absolute risk reduction is the parameter that allowed computing the number needed to treat. The absolute risk reduction is compute when the experimental treatment reduces the risk for an undesirable outcome/event. In medical literature when the absolute risk reduction is report with its confidence intervals, the method used is the asymptotic one, even if it is well know that may be inadequate. The aim of this paper is to introduce and assess nine methods of computing confidence intervals for absolute risk reduction and absolute risk reduction – like function.Computer implementations of the methods use the PHP language. Methods comparison uses the experimental errors, the standard deviations, and the deviation relative to the imposed significance level for specified sample sizes. Six methods of computing confidence intervals for absolute risk reduction and absolute risk reduction-like functions were assessed using random binomial variables and random sample sizes.The experiments shows that the ADAC, and ADAC1 methods obtains the best overall performance of computing confidence intervals for absolute risk reduction.
Tarnowsky, Terence J
2013-01-01
A study of the first four moments (mean, variance, skewness, and kurtosis) and their products ($\\kappa\\sigma^{2}$ and $S\\sigma$) of the net-charge and net-proton distributions in Au+Au collisions at $\\sqrt{\\rm s_{NN}}$ = 7.7-200 GeV from HIJING simulations has been carried out. It is seen that a Poisson does not effectively describe the actual distributions of positive and negative particles (or protons and anti-protons). A discrete probability distribution that effectively describes the raw distributions is the negative binomial (or binomial) distribution (NBD/BD). The NBD/BD have been used to characterize particle production in high-energy particle and nuclear physics. Differences between $\\kappa\\sigma^{2}$ and the Poisson assumption of a factor of four (for net-charge) and 40% (for net-protons) can be accounted for by the NBD/BD. This is the first application of the NBD/BD to describe the behavior of the higher moments of net-charge and net-proton distributions in nucleus-nucleus collisions.
Tarnowsky, Terence J.; Westfall, Gary D.
2013-07-01
A study of the first four moments (mean, variance, skewness, and kurtosis) and their products (κσ2 and Sσ) of the net-charge and net-proton distributions in Au + Au collisions at √{sNN} = 7.7- 200 GeV from HIJING simulations has been carried out. The skewness and kurtosis and the collision volume independent products κσ2 and Sσ have been proposed as sensitive probes for identifying the presence of a QCD critical point. A discrete probability distribution that effectively describes the separate positively and negatively charged particle (or proton and anti-proton) multiplicity distributions is the negative binomial (or binomial) distribution (NBD/BD). The NBD/BD has been used to characterize particle production in high-energy particle and nuclear physics. Their application to the higher moments of the net-charge and net-proton distributions is examined. Differences between κσ2 and a statistical Poisson assumption of a factor of four (for net-charge) and 40% (for net-protons) can be accounted for by the NBD/BD. This is the first application of the properties of the NBD/BD to describe the behavior of the higher moments of net-charge and net-proton distributions in nucleus-nucleus collisions.
Manté, Claude; Kidé, Oumar, Saikou; Yao, Anne-Françoise; Mérigot, Bastien
2016-01-01
International audience A frequent issue in the study of species abundance consists in modeling empirical distributions of repeated counts by parametric probability distributions. In this setting, it is desirable that the chosen family of distributions is exible enough to take into account very diverse patterns, and that its parameters possess clear biological/ecological meanings. This is the case of the Negative Binomial distribution, chosen in this work for modeling counts of marine shes ...
Ghosh, Premomoy
2012-01-01
Experiments at the Large Hadron Collider (LHC) have measured multiplicity distributions in proton-proton collisions at a new domain of center-of-mass energy ($\\sqrt {s}$) in limited pseudorapidity intervals. We analyze multiplicity distribution data of proton-proton collisions at LHC energies as measured by the Compact Muon Solenoid (CMS) experiment in terms of characteristic parameters of the Negative Binomial Distribution (NBD) function that has played a significant role in describing multi...
Xiao, Chuan-Le; Chen, Xiao-Zhou; Du, Yang-Li; Sun, Xuesong; Zhang, Gong; He, Qing-Yu
2013-01-01
Mass spectrometry has become one of the most important technologies in proteomic analysis. Tandem mass spectrometry (LC-MS/MS) is a major tool for the analysis of peptide mixtures from protein samples. The key step of MS data processing is the identification of peptides from experimental spectra by searching public sequence databases. Although a number of algorithms to identify peptides from MS/MS data have been already proposed, e.g. Sequest, OMSSA, X!Tandem, Mascot, etc., they are mainly based on statistical models considering only peak-matches between experimental and theoretical spectra, but not peak intensity information. Moreover, different algorithms gave different results from the same MS data, implying their probable incompleteness and questionable reproducibility. We developed a novel peptide identification algorithm, ProVerB, based on a binomial probability distribution model of protein tandem mass spectrometry combined with a new scoring function, making full use of peak intensity information and, thus, enhancing the ability of identification. Compared with Mascot, Sequest, and SQID, ProVerB identified significantly more peptides from LC-MS/MS data sets than the current algorithms at 1% False Discovery Rate (FDR) and provided more confident peptide identifications. ProVerB is also compatible with various platforms and experimental data sets, showing its robustness and versatility. The open-source program ProVerB is available at http://bioinformatics.jnu.edu.cn/software/proverb/ . PMID:23163785
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Patricio Peña-Rehbein
2012-03-01
Full Text Available Nematodes of the genus Anisakis have marine fishes as intermediate hosts. One of these hosts is Thyrsites atun, an important fishery resource in Chile between 38 and 41° S. This paper describes the frequency and number of Anisakis nematodes in the internal organs of Thyrsites atun. An analysis based on spatial distribution models showed that the parasites tend to be clustered. The variation in the number of parasites per host could be described by the negative binomial distribution. The maximum observed number of parasites was nine parasites per host. The environmental and zoonotic aspects of the study are also discussed.Nematóides do gênero Anisakis têm nos peixes marinhos seus hospedeiros intermediários. Um desses hospedeiros é Thyrsites atun, um importante recurso pesqueiro no Chile entre 38 e 41° S. Este artigo descreve a freqüência e o número de nematóides Anisakis nos órgãos internos de Thyrsites atun. Uma análise baseada em modelos de distribuição espacial demonstrou que os parasitos tendem a ficar agrupados. A variação numérica de parasitas por hospedeiro pôde ser descrita por distribuição binomial negativa. O número máximo observado de parasitas por hospedeiro foi nove. Os aspectos ambientais e zoonóticos desse estudo também serão discutidos.
An Approximate Interval Estimate on the Parameter of Negative Binomial Distribution%负二项分布参数的一类近似区间估计
Institute of Scientific and Technical Information of China (English)
姜培华
2012-01-01
借助负二项分布和卡方分布的极限关系，推导给出当参数P较小条件下的近似区间估计，并通过数值例子介绍了此区间估计方法的应用．%An approximate interval estimate for small was gained with the limit relationship of negative binomi- al distribution and the chi - square distribution ; Finally, the method of interval estimate was studied and illustration was shown by examples.
Distribusi Markov-Binomial Negatif
Widyasari, Rina
2015-01-01
The way to find a new distribution of random variables is defining the distribution which associated with Markov chain. In this research, researcher defines all the random variables identically independent distributed negative binomial distribution and form a Markov chain. Suppose that Xn is a sequence of Bernoulli trials that if 1 occurs means ”success” and 0 occurs means ”failure”. Nb(s) defined as random variables sth success in n trials. Each trial form a Markov chain, in n...
Biyajima, M.; OSADA, T; Takei, K.
1998-01-01
A pure birth stochastic process with several initial conditions is considered.We analyze multiplicity distributions of e^+e^- collisions and e-p collisions, usigthe Modified Negative Binomial Distribution (MNBD) and the Laguerre-type distribution. Several multiplicity distributions show the same minimum \\chi^2's values in analyses by means of two formulas: In these cases, we find that a parameter N contained in the MNBD becomes to be large. Taking large N limit in the MNBD, we find that the L...
Ghosh, Premomoy
2012-01-01
Experiments at the Large Hadron Collider (LHC) have measured multiplicity distributions in proton-proton collisions at a new domain of center-of-mass energy ($\\sqrt {s}$) in limited pseudorapidity intervals. We analyze multiplicity distribution data of proton-proton collisions at LHC energies as measured by the Compact Muon Solenoid (CMS) experiment in terms of characteristic parameters of the Negative Binomial Distribution (NBD) function that has played a significant role in describing multiplicity distribution data of particle production in high energy physics experiments, in the pre-LHC energy-range, in various kinds of collisions for a wide range of collision energy and for different kinematic ranges. Beside a single NBD, we apply the formalism of weighted superposition of two NBDs to examine if the multiplicity distribution data of CMS could be better explained. The weighted superposition of two NBDs indeed explain the distribution data better at the highest available LHC energy and in large interval of ...
Jackwerth, Jens Carsten
1996-01-01
We consider the problem of consistently pricing new options given the prices of related options on the same stock. The Black-Scholes formula and standard binomial trees can only accommodate one related European option which then effectively specifies the volatility parameter. Implied binomial trees can accommodate only related European options with the same time-to-expiration.The generalized binomial trees introduced here can accommodate any kind of related options (European, American, or exo...
Institute of Scientific and Technical Information of China (English)
王丙参; 何万生; 戴宁
2011-01-01
This article discusses the properties and promotion of the two basic negative binomial distributions,gives closed of conditional probabilities and a non-classical confidence interval estimate under the first negative binomial distribution,discusses the relationship between the second negative binomial distribution to poisson distribution.%研究了负二项分布的两个基本模型及推广,得到第一类负二项分布条件概率具有封闭性且给出参数的一个非经典置信区间估计,特别研究了第二类负二项分布与泊松分布的关系。
Negative Binomial States of Quantized Radiation Fields
Fu, Hong-Chen; Sasaki, Ryu
1996-01-01
We introduce the negative binomial states with negative binomial distribution as their photon number distribution. They reduce to the ordinary coherent states and Susskind-Glogower phase states in different limits. The ladder and displacement operator formalisms are found and they are essentially the Perelomov's su(1,1) coherent states via its Holstein-Primakoff realisation. These states exhibit strong squeezing effect and they obey the super-Poissonian statistics. A method to generate these ...
Negative Binomial States of Quantized Radiation Fields
Fu, H C; Fu, Hong-Chen; Sasaki, Ryu
1996-01-01
We introduce the negative binomial states with negative binomial distribution as their photon number distribution. They reduce to the ordinary coherent states and Susskind-Glogower phase states in different limits. The ladder and displacement operator formalisms are found and they are essentially the Perelomov's su(1,1) coherent states via its Holstein-Primakoff realisation. These states exhibit strong squeezing effect and they obey the super-Poissonian statistics. A method to generate these states is proposed.
Ghosh, Premomoy
2012-03-01
Experiments at the Large Hadron Collider (LHC) have measured multiplicity distributions in proton-proton collisions at a new domain of center-of-mass energy (s) in limited pseudorapidity intervals. We analyze multiplicity distribution data of proton-proton collisions at LHC energies as measured by the Compact Muon Solenoid (CMS) experiment in terms of characteristic parameters of the negative binomial distribution (NBD) function that has played a significant role in describing multiplicity distribution data of particle production in high-energy physics experiments, in the pre-LHC energy range, in various kinds of collisions for a wide range of collision energy and for different kinematic ranges. Beside a single NBD, we apply the formalism of weighted superposition of two NBDs to examine if the multiplicity distribution data of CMS could be better explained. The weighted superposition of two NBDs indeed explains the distribution data better at the highest available LHC energy and in large intervals of phase space. The two-NBD formalism further reveals that the energy invariance of the multiplicity distribution of the soft component of particle production in hadronic collisions is valid at LHC also, as it is at RHIC and Tevatron. We analyze the data further in terms of clan parameters in the framework of the two-NBD model.
Two Interval Estimates on the Parameter of Negative Binomial Distribution%负二项分布参数的两种区间估计
Institute of Scientific and Technical Information of China (English)
姜培华; 范国良
2012-01-01
研究了负二项分布参数的区间估计方法,给出其两种区间估计方法.首先给出负二项分布参数的精确区间估计方法；其次给出大样本近似区间估计方法.最后通过数值例子介绍这些区间估计方法的应用.%The methods of interval estimate on the parameter of negative binomial distribution have been studied. Two methods are given. Firstly, the accurate interval estimate is put forward ; secondly, large sample approximate inter-val estimate is gained; Finally,these methods of interval estimate are studied and illustration is shown by examples.
基于β-二项分布的结构易损性分析%Structural fragility estimation with beta-binomial distribution
Institute of Scientific and Technical Information of China (English)
刘骁骁; 吴子燕; 王其昂
2014-01-01
易损性曲线建立过程中受激励不确定性和结构参数不确定性的影响，会引起结构或构件观测结果的统计相关性。为此，本文提出基于β-二项分布的结构易损性分析方法。该方法根据性能量化指标阈值和 Monte Carlo模拟确定震后观测结果，采用β-二项分布探讨震后观测值的统计相关性；结合对数回归模型，推导了改进β-二项分布的累积分布函数，计算结构失效概率；通过累积对数正态分布拟合易损性曲线，比较了观测失效样本数与观测失效概率统计相关性对易损性的影响，并与未考虑统计相关性的传统易损性曲线作对比。某8层钢筋混凝土框架-剪力墙结构的算例表明，考虑统计相关性的易损性较传统易损性偏大，且结构遭受8度以上地震作用时，考虑失效样本数统计相关性的易损性使预测结果更为保守，利于工程安全。%The uncertainty of seismic excitation and structural parameters in the process of establishing fragility curves leads to statistical dependence among observations,which has been neglected in past applications.In this paper,a new methodology based on beta-binomial distribution to calculate structural fragility is presented.Observations indicating the states (failure or survival)are confirmed via quantita-tive indicators threshold as well as Monte Carlo after each earthquake.Beta-Binomial distribution is ad-dressed to discuss the statistical dependence among observations.Improved cumulative beta-binomial dis-tribution function is derivation to calculate failure probability combined with logistic regression model. Seismic vulnerability curve can be fitted by means of cumulative lognormal distribution,which is com-pared with traditional fragility that of neglecting statistical dependence among observations and fragility curve considering statistical dependence among observed failure rates.A seat eight floors reinforced con
Option pricing for the transformed‐binomial class
António Câmara; San‐Lin Chung
2006-01-01
This article generalizes the seminal Cox‐Ross‐Rubinstein (1979) binomial option pricing model to all members of the class of transformed‐binomial pricing processes. The investigation addresses issues related with asset pricing modeling, hedging strategies, and option pricing. Formulas are derived for (a) replicating or hedging portfolios, (b) risk‐neutral transformed‐binomial probabilities, (c) limiting transformed‐normal distributions, and (d) the value of contingent claims, including limiti...
Directory of Open Access Journals (Sweden)
Anwer Khurshid
2014-12-01
Full Text Available Measurement error effect on the power of control charts for zero truncated Poisson distribution and ratio of two Poisson distributions are recently studied by Chakraborty and Khurshid (2013a and Chakraborty and Khurshid (2013b respectively. In this paper, in addition to the expression for the power of control chart for ZTBD based on standardized normal variate is obtained, numerical calculations are presented to see the effect of errors on the power curve. To study the sensitivity of the monitoring procedure, average run length (ARL is also considered.
International Nuclear Information System (INIS)
Fluctuations in pseudorapidity of charged particles from central (ZCAL) collisions of 16O + Cu at 14.6 A·GeV/c have been analyzed by the E802 Collaboration using the method of normalized factorial moments as a function of the interval Δη. In agreement with previous measurements, an apparent power-law growth of moments with decreasing interval is observed down to Δη ∼ 0.1. Experience with ET distributions suggests that fluctuations of multiplicity and transverse energy can be well described by Gamma or Negative Binomial Distributions (NBD) and excellent fits to NBD were obtained in all Δη bins. The κ parameter of the NBD fit was found to increase linearly with the Δη interval, which due to the well known property of the NBD under convolution, indicates that the multiplicity distributions in adjacent bins of pseudorapidity Δη ∼ 0.1 are largely statistically independent
Sperling, J.; Vogel, W; Agarwal, G. S.
2012-01-01
The click statistics from on-off detector systems is quite different from the counting statistics of the more traditional detectors. This necessitates introduction of new parameters to characterize the nonclassicality of fields from measurements using on-off detectors. To properly replace the Mandel Q_M parameter, we introduce a parameter Q_B. A negative value represents a sub-binomial statistics. This is possible only for quantum fields, even for super-Poisson light. It eliminates the proble...
Real and imaginary negative binomial states
Liao, Jing; Wang, Xiaoguang; Wu, Ling-An; Pan, Shao-Hua
2001-10-01
The real and imaginary negative binomial states formed by a superposition of the negative binomial states are introduced. The sub-Poissonian statistics, Wigner function and squeezing properties of the real and imaginary states are studied in detail. The oscillatory character of the photon distribution due to the quantum interference between the two components is shown. Moreover, we find that these states are real and imaginary nonlinear Schrödinger cat states and give the corresponding ladder operator formalisms. We also discuss how to generate these general real quantum superposition states based on the intensity-dependent Jaynes-Cummings model.
On a fractional binomial process
Cahoy, Dexter O.; Polito, Federico
2013-01-01
The classical binomial process has been studied by \\citet{jakeman} (and the references therein) and has been used to characterize a series of radiation states in quantum optics. In particular, he studied a classical birth-death process where the chance of birth is proportional to the difference between a larger fixed number and the number of individuals present. It is shown that at large times, an equilibrium is reached which follows a binomial process. In this paper, the classical binomial p...
Augment-and-Conquer Negative Binomial Processes
Zhou, Mingyuan; Carin, Lawrence
2012-01-01
By developing data augmentation methods unique to the negative binomial (NB) distribution, we unite seemingly disjoint count and mixture models under the NB process framework. We develop fundamental properties of the models and derive efficient Gibbs sampling inference. We show that the gamma-NB process can be reduced to the hierarchical Dirichlet process with normalization, highlighting its unique theoretical, structural and computational advantages. A variety of NB processes with distinct s...
Fourier Spectra of Binomial APN Functions
Bracken, Carl; Markin, Nadya; McGuire, Gary
2008-01-01
In this paper we compute the Fourier spectra of some recently discovered binomial APN functions. One consequence of this is the determination of the nonlinearity of the functions, which measures their resistance to linear cryptanalysis. Another consequence is that certain error-correcting codes related to these functions have the same weight distribution as the 2-error-correcting BCH code. Furthermore, for fields of odd degree, our results provide an alternative proof of the APN property of the functions.
Stein factors for negative binomial approximation in Wasserstein distance
Barbour, A. D.; Gan, H.L.; Xia, A
2015-01-01
The paper gives the bounds on the solutions to a Stein equation for the negative binomial distribution that are needed for approximation in terms of the Wasserstein metric. The proofs are probabilistic, and follow the approach introduced in Barbour and Xia (Bernoulli 12 (2006) 943-954). The bounds are used to quantify the accuracy of negative binomial approximation to parasite counts in hosts. Since the infectivity of a population can be expected to be proportional to its total parasite burde...
Binomial expansions modulo prime powers
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Paul W. Haggard
1980-01-01
Full Text Available In this note a result is given and proved concerning binomial expansions modulo prime powers. In the proof congruence modulo prime powers is generalized to the rational numbers via valuations.
A new bivariate negative binomial regression model
Faroughi, Pouya; Ismail, Noriszura
2014-12-01
This paper introduces a new form of bivariate negative binomial (BNB-1) regression which can be fitted to bivariate and correlated count data with covariates. The BNB regression discussed in this study can be fitted to bivariate and overdispersed count data with positive, zero or negative correlations. The joint p.m.f. of the BNB1 distribution is derived from the product of two negative binomial marginals with a multiplicative factor parameter. Several testing methods were used to check overdispersion and goodness-of-fit of the model. Application of BNB-1 regression is illustrated on Malaysian motor insurance dataset. The results indicated that BNB-1 regression has better fit than bivariate Poisson and BNB-2 models with regards to Akaike information criterion.
Quentin Noirhomme; Damien Lesenfants; Francisco Gomez; Andrea Soddu; Jessica Schrouff; Gaëtan Garraux; André Luxen; Christophe Phillips; Steven Laureys
2014-01-01
Multivariate classification is used in neuroimaging studies to infer brain activation or in medical applications to infer diagnosis. Their results are often assessed through either a binomial or a permutation test. Here, we simulated classification results of generated random data to assess the influence of the cross-validation scheme on the significance of results. Distributions built from classification of random data with crossvalidation did not follow the binomial distribution. The binomi...
Institute of Scientific and Technical Information of China (English)
王琪; 李玮
2011-01-01
The Bayesian and hierarchical Bayesian estimators of reliability of negative binomial distribution are obtained, and the E Bayesian estimator is also discussed by E Bayesian approach. Finally, a numberical example is given to compare the former three estmators, and the contusion shows that the E Bayesian estimator is better than the hierarchical Bayesian estimator.%在一类新的加权平方损失函数下,给出了负二项分布可靠度的Bayes和多层Bayes估计,并利用EBayes方法给出了负二项分布可靠度的E Bayes估计.针对得到的3种估计,给出了数值模拟,结果表明:EBayes估计比多层Bayes估计优良.
Mark Rubinstein.
1997-01-01
This paper develops a simple technique for valuing European and American derivatives with underlying asset risk-neutral returns which depart from lognormal in terms of prespecified non-zero skewness and greater-than-three kurtosis. Instead of specifying the entire risk-neutral distribution by the riskless return and volatility (as in the Black-Scholes case), this distribution is specified by its third and fourth central moments as well. An Edgeworth expansion is used to transform a standard b...
Transform methods for testing the negative binomial hypothesis
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Simos G. Meintanis
2007-10-01
Full Text Available We employ the empirical probability generating function in constructing a goodness-of-fit test for negative binomial distributions. The proposed tests, which are formed as weighted integrals, are shown to be consistent and their asymptotic null distribution is investigated. As the decay of the weight function tends to infinity, limit statistics are obtained. A small simulation study is presented.
Transform methods for testing the negative binomial hypothesis
Meintanis, Simos G.
2007-01-01
We employ the empirical probability generating function in constructing a goodness-of-fit test for negative binomial distributions. The proposed tests, which are formed as weighted integrals, are shown to be consistent and their asymptotic null distribution is investigated. As the decay of the weight function tends to infinity, limit statistics are obtained. A small simulation study is presented.
Institute of Scientific and Technical Information of China (English)
姜培华; 纪习习; 吴玲
2014-01-01
In terms of prior distribution of Beta distribution, the Bayesian estimation method on the unknown parame-ter θ of negative binomial distribution was studied. By means of the relations between Beta distribution and the F dis-tribution the general posterior interval estimation of parameter θ was given, and the shortest posterior interval estima-tion by means of conditional extreme was gained. By comparing the discussion analysis and numerical examples den-sity curve shape of the different parameters, it was concluded that in the case of small samples, the shortest confi-dence interval estimation method is worth using.%研究了在先验分布为贝塔分布下，负二项分布未知参数θ的贝叶斯区间估计方法。借助Beta分布与F分布的关系给出了参数θ的一般后验区间估计，并给出了参数θ的最短后验区间估计的条件极值解法。通过对参数取值不同的密度曲线形状的讨论分析和数值实例对比，得出结论：在小样本情况下，最短置信区间估计方法值得采用。
Zero inflated negative binomial-generalized exponential distributionand its applications
Sirinapa Aryuyuen; Winai Bodhisuwan; Thidaporn Supapakorn
2014-01-01
In this paper, we propose a new zero inflated distribution, namely, the zero inflated negative binomial-generalized exponential (ZINB-GE) distribution. The new distribution is used for count data with extra zeros and is an alternative for data analysis with over-dispersed count data. Some characteristics of the distribution are given, such as mean, variance, skewness, and kurtosis. Parameter estimation of the ZINB-GE distribution uses maximum likelihood estimation (MLE) method. Simul...
Non-Commutative Q-Binomial Formula
Nalci, Sengul; Pashaev, Oktay
2012-01-01
In this paper, we found new q-binomial formula for Q-commutative operators. Expansion coefficients in this formula are given by q-binomial coefficients with two bases (q,Q), determined by Q-commutative q-Pascal triangle. Our formula generalizes all well-known binomial formulas in the form of Newton, Gauss, symmetrical, non-commutative and Binet-Fibonacci binomials. By our non-commutative q-binomial, we introduce q-analogue of function of two non-commutative variables, which could be used in s...
Zero inflated negative binomial-generalized exponential distributionand its applications
Directory of Open Access Journals (Sweden)
Sirinapa Aryuyuen
2014-08-01
Full Text Available In this paper, we propose a new zero inflated distribution, namely, the zero inflated negative binomial-generalized exponential (ZINB-GE distribution. The new distribution is used for count data with extra zeros and is an alternative for data analysis with over-dispersed count data. Some characteristics of the distribution are given, such as mean, variance, skewness, and kurtosis. Parameter estimation of the ZINB-GE distribution uses maximum likelihood estimation (MLE method. Simulated and observed data are employed to examine this distribution. The results show that the MLE method seems to have high efficiency for large sample sizes. Moreover, the mean square error of parameter estimation is increased when the zero proportion is higher. For the real data sets, this new zero inflated distribution provides a better fit than the zero inflated Poisson and zero inflated negative binomial distributions.
Numerics of implied binomial trees
Härdle, Wolfgang Karl; Myšičková, Alena
2008-01-01
Market option prices in last 20 years confirmed deviations from the Black and Scholes (BS) models assumptions, especially on the BS implied volatility. Implied binomial trees (IBT) models capture the variations of the implied volatility known as \\volatility smile". They provide a discrete approximation to the continuous risk neutral process for the underlying assets. In this paper, we describe the numerical construction of IBTs by Derman and Kani (DK) and an alternative method by Barle and Ca...
Negative Binomial GAM and GAMM to Analyse Amphibian Roadkills
Zuur, Alain; Mira, António; Carvalho, Filipe; Ieno, Elena; Saveliev, A.A.; Smith, G.M.; Walker, N. J.
2009-01-01
This chapter analyses amphibian fatalities along a road in Portugal. The data are counts of kills making a Gaussian distribution unlikely; restricting our choice of techniques. We began with generalised linear models (GLM) and generalised addi- tive models (GAM) with a Poisson distribution, but these models were overdis- persed. To solve this, you can either apply a quasi-Poisson GLM or GAM, or use the negative binomial distribution (Chapter 9). In this particular example, eith...
Generalized Negative Binomial Processes and the Representation of Cluster Structures
Zhou, Mingyuan
2013-01-01
The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset of the sample to be dependent on the sample size, a feature not presented in a partition structure. A generalized negative binomial process count-mixture model is proposed to generate a cluster structure, where in the prior the number of clusters is finite...
Negative Binomial Process Count and Mixture Modeling.
Zhou, Mingyuan; Carin, Lawrence
2015-02-01
The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an NB process for count modeling. A draw from the NB process consists of a Poisson distributed finite number of distinct atoms, each of which is associated with a logarithmic distributed number of data samples. We reveal relationships between various count- and mixture-modeling distributions and construct a Poisson-logarithmic bivariate distribution that connects the NB and Chinese restaurant table distributions. Fundamental properties of the models are developed, and we derive efficient Bayesian inference. It is shown that with augmentation and normalization, the NB process and gamma-NB process can be reduced to the Dirichlet process and hierarchical Dirichlet process, respectively. These relationships highlight theoretical, structural, and computational advantages of the NB process. A variety of NB processes, including the beta-geometric, beta-NB, marked-beta-NB, marked-gamma-NB and zero-inflated-NB processes, with distinct sharing mechanisms, are also constructed. These models are applied to topic modeling, with connections made to existing algorithms under Poisson factor analysis. Example results show the importance of inferring both the NB dispersion and probability parameters. PMID:26353243
A Class of Binomial Permutation Polynomials
Tu, Ziran; Zeng, Xiangyong; Hu, Lei; Li, Chunlei
2013-01-01
In this note, a criterion for a class of binomials to be permutation polynomials is proposed. As a consequence, many classes of binomial permutation polynomials and monomial complete permutation polynomials are obtained. The exponents in these monomials are of Niho type.
Priors for Random Count Matrices Derived from a Family of Negative Binomial Processes
Zhou, Mingyuan; Padilla, Oscar Hernan Madrid; SCOTT, James G.
2014-01-01
We define a family of probability distributions for random count matrices with a potentially unbounded number of rows and columns. The three distributions we consider are derived from the gamma-Poisson, gamma-negative binomial, and beta-negative binomial processes. Because the models lead to closed-form Gibbs sampling update equations, they are natural candidates for nonparametric Bayesian priors over count matrices. A key aspect of our analysis is the recognition that, although the random co...
Stochastic analysis of complex reaction networks using binomial moment equations.
Barzel, Baruch; Biham, Ofer
2012-09-01
The stochastic analysis of complex reaction networks is a difficult problem because the number of microscopic states in such systems increases exponentially with the number of reactive species. Direct integration of the master equation is thus infeasible and is most often replaced by Monte Carlo simulations. While Monte Carlo simulations are a highly effective tool, equation-based formulations are more amenable to analytical treatment and may provide deeper insight into the dynamics of the network. Here, we present a highly efficient equation-based method for the analysis of stochastic reaction networks. The method is based on the recently introduced binomial moment equations [Barzel and Biham, Phys. Rev. Lett. 106, 150602 (2011)]. The binomial moments are linear combinations of the ordinary moments of the probability distribution function of the population sizes of the interacting species. They capture the essential combinatorics of the reaction processes reflecting their stoichiometric structure. This leads to a simple and transparent form of the equations, and allows a highly efficient and surprisingly simple truncation scheme. Unlike ordinary moment equations, in which the inclusion of high order moments is prohibitively complicated, the binomial moment equations can be easily constructed up to any desired order. The result is a set of equations that enables the stochastic analysis of complex reaction networks under a broad range of conditions. The number of equations is dramatically reduced from the exponential proliferation of the master equation to a polynomial (and often quadratic) dependence on the number of reactive species in the binomial moment equations. The aim of this paper is twofold: to present a complete derivation of the binomial moment equations; to demonstrate the applicability of the moment equations for a representative set of example networks, in which stochastic effects play an important role. PMID:23030885
Combinatorial clustering and the beta negative binomial process
Broderick, Tamara; Mackey, Lester; Paisley, John; Jordan, Michael I
2011-01-01
We develop a Bayesian nonparametric approach to a general family of latent class problems in which individuals can belong simultaneously to multiple classes and where each class can be exhibited multiple times by an individual. We introduce a combinatorial stochastic process known as the negative binomial process (NBP) as an infinite-dimensional prior appropriate for such problems. We show that the NBP is conjugate to the beta process, and we characterize the posterior distribution under the ...
Sampling from a couple of positively correlated binomial variables
Catalani, Mario
2002-01-01
We know that the marginals in a multinomial distribution are binomial variates exhibiting a negative correlation. But we can construct two linear combinations of such marginals in such a way to obtain a positive correlation. We discuss the restrictions that are to be imposed on the parameters of the given marginals to accomplish such a result. Next we discuss the regression function, showing that it is a linear function but not homoscedastic.
A Note on Bayesian Estimation for the Negative-Binomial Model
L. Lio, Y.
2009-01-01
2000 Mathematics Subject Classification: 62F15. The Negative Binomial model, which is generated by a simple mixture model, has been widely applied in the social, health and economic market prediction. The most commonly used methods were the maximum likelihood estimate (MLE) and the moment method estimate (MME). Bradlow et al. (2002) proposed a Bayesian inference with beta-prime and Pearson Type VI as priors for the negative binomial distribution. It is due to the complicated posterior dens...
Higher Order Asymptotics for Negative Binomial Regression Inferences from RNA-Sequencing Data
Di, Yanming; Emerson, Sarah C.; Daniel W Schafer; Jeffrey A Kimbrel; Chang, Jeff H
2013-01-01
RNA sequencing (RNA-Seq) is the current method of choice for characterizing transcriptomes and quantifying gene expression changes. This next generation sequencing-based method provides unprecedented depth and resolution. The negative binomial (NB) probability distribution has been shown to be a useful model for frequencies of mapped RNA-Seq reads and consequently provides a basis for statistical analysis of gene expression. Negative binomial exact tests are available for two-g...
Newton Binomial Formulas in Schubert Calculus
Cordovez, Jorge; Gatto, Letterio; Santiago, Taise
2008-01-01
We prove Newton's binomial formulas for Schubert Calculus to determine numbers of base point free linear series on the projective line with prescribed ramification divisor supported at given distinct points.
Nonparametric Bayesian Negative Binomial Factor Analysis
Zhou, Mingyuan
2016-01-01
A common approach to analyze an attribute-instance count matrix, an element of which represents how many times an attribute appears in an instance, is to factorize it under the Poisson likelihood. We show its limitation in capturing the tendency for an attribute present in an instance to both repeat itself and excite related ones. To address this limitation, we construct negative binomial factor analysis (NBFA) to factorize the matrix under the negative binomial likelihood, and relate it to a...
Computation of Greeks using Binomial Tree
Yoshifumi Muroi; Shintaro Suda
2014-01-01
This paper proposes a new efficient algorithm for the computation of Greeks for options using the binomial tree. We also show that Greeks for European options introduced in this article are asymptotically equivalent to the discrete version of Malliavin Greeks. This fact enables us to show that our Greeks converge to Malliavin Greeks in the continuous time model. The computation algorithms of Greeks for American options using the binomial tree is also given in this article. There are three adv...
A mixed time series model of binomial counts
Khoo, Wooi Chen; Ong, Seng Huat
2015-10-01
Continuous time series modelling has been an active research in the past few decades. However, time series data in terms of correlated counts appear in many situations such as the counts of rainy days and access downloading. Therefore, the study on count data has become popular in time series modelling recently. This article introduces a new mixture model, which is an univariate non-negative stationary time series model with binomial marginal distribution, arising from the combination of the well-known binomial thinning and Pegram's operators. A brief review of important properties will be carried out and the EM algorithm is applied in parameter estimation. A numerical study is presented to show the performance of the model. Finally, a potential real application will be presented to illustrate the advantage of the new mixture model.
Exact Group Sequential Methods for Estimating a Binomial Proportion
Directory of Open Access Journals (Sweden)
Zhengjia Chen
2013-01-01
Full Text Available We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence level. In particular, we establish the uniform controllability of coverage probability and the asymptotic optimality for such a family of sampling schemes. Our theoretical results establish the possibility that the parameters of this family of sampling schemes can be determined so that the prescribed level of confidence is guaranteed with little waste of samples. Analytic bounds for the cumulative distribution functions and expectations of sample numbers are derived. Moreover, we discuss the inherent connection of various sampling schemes. Numerical issues are addressed for improving the accuracy and efficiency of computation. Computational experiments are conducted for comparing sampling schemes. Illustrative examples are given for applications in clinical trials.
PENERAPAN REGRESI BINOMIAL NEGATIF UNTUK MENGATASI OVERDISPERSI PADA REGRESI POISSON
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PUTU SUSAN PRADAWATI
2013-09-01
Full Text Available Poisson regression was used to analyze the count data which Poisson distributed. Poisson regression analysis requires state equidispersion, in which the mean value of the response variable is equal to the value of the variance. However, there are deviations in which the value of the response variable variance is greater than the mean. This is called overdispersion. If overdispersion happens and Poisson Regression analysis is being used, then underestimated standard errors will be obtained. Negative Binomial Regression can handle overdispersion because it contains a dispersion parameter. From the simulation data which experienced overdispersion in the Poisson Regression model it was found that the Negative Binomial Regression was better than the Poisson Regression model.
Directory of Open Access Journals (Sweden)
Quentin Noirhomme
2014-01-01
Full Text Available Multivariate classification is used in neuroimaging studies to infer brain activation or in medical applications to infer diagnosis. Their results are often assessed through either a binomial or a permutation test. Here, we simulated classification results of generated random data to assess the influence of the cross-validation scheme on the significance of results. Distributions built from classification of random data with cross-validation did not follow the binomial distribution. The binomial test is therefore not adapted. On the contrary, the permutation test was unaffected by the cross-validation scheme. The influence of the cross-validation was further illustrated on real-data from a brain–computer interface experiment in patients with disorders of consciousness and from an fMRI study on patients with Parkinson disease. Three out of 16 patients with disorders of consciousness had significant accuracy on binomial testing, but only one showed significant accuracy using permutation testing. In the fMRI experiment, the mental imagery of gait could discriminate significantly between idiopathic Parkinson's disease patients and healthy subjects according to the permutation test but not according to the binomial test. Hence, binomial testing could lead to biased estimation of significance and false positive or negative results. In our view, permutation testing is thus recommended for clinical application of classification with cross-validation.
Noirhomme, Quentin; Lesenfants, Damien; Gomez, Francisco; Soddu, Andrea; Schrouff, Jessica; Garraux, Gaëtan; Luxen, André; Phillips, Christophe; Laureys, Steven
2014-01-01
Multivariate classification is used in neuroimaging studies to infer brain activation or in medical applications to infer diagnosis. Their results are often assessed through either a binomial or a permutation test. Here, we simulated classification results of generated random data to assess the influence of the cross-validation scheme on the significance of results. Distributions built from classification of random data with cross-validation did not follow the binomial distribution. The binomial test is therefore not adapted. On the contrary, the permutation test was unaffected by the cross-validation scheme. The influence of the cross-validation was further illustrated on real-data from a brain–computer interface experiment in patients with disorders of consciousness and from an fMRI study on patients with Parkinson disease. Three out of 16 patients with disorders of consciousness had significant accuracy on binomial testing, but only one showed significant accuracy using permutation testing. In the fMRI experiment, the mental imagery of gait could discriminate significantly between idiopathic Parkinson's disease patients and healthy subjects according to the permutation test but not according to the binomial test. Hence, binomial testing could lead to biased estimation of significance and false positive or negative results. In our view, permutation testing is thus recommended for clinical application of classification with cross-validation. PMID:24936420
Bayesian Estimation Based on Rayleigh Progressive Type II Censored Data with Binomial Removals
Directory of Open Access Journals (Sweden)
Reza Azimi
2013-01-01
the number of units removed at each failure time has a binomial distribution. We use the maximum likelihood and Bayesian procedures to obtain the estimators of parameter and reliability function of Rayleigh distribution. We also construct the confidence intervals for the parameter of Rayleigh distribution. Monte Carlo simulation method is used to generate a progressive type II censored data with binomial removals from Rayleigh distribution, and then these data are used to compute the point and interval estimations of the parameter and compare both the methods used with different random schemes.
Solis, Adriano O.; Schmidt, Charles P.; Conerly, Michael D.
2007-09-01
Graves (1996) developed a multi-echelon inventory model and used a negative binomial distribution to approximate the distribution of a random variable in the model. Two earlier multi-echelon inventory studies (Graves, 1985; Lee and Moinzadeh, 1987) have similarly used negative binomial approximations. Only computational evidence has been offered in support of the approximations. We provide, for the latest model (Graves, 1996), a mathematical analysis of the effectiveness of such an approximation.
The Binomial - Medicine/Art [In Bulgarian
Directory of Open Access Journals (Sweden)
E. Pavlov
2008-12-01
Full Text Available The article considers the binomial – medicine/art. Medical treatment of body should be combined with the medical treatment of soul. ‘A sound mind in a sound body’ can be achieved when art supports medicine. Semiotic aspects of medicine are discussed. The introduction of such ideas to medical education is recommended.
Large Deviation Results for Generalized Compound Negative Binomial Risk Models
Institute of Scientific and Technical Information of China (English)
Fan-chao Kong; Chen Shen
2009-01-01
In this paper we extend and improve some results of the large deviation for random sums of random variables.Let {Xn;n≥1} be a sequence of non-negative,independent and identically distributed random variables with common heavy-tailed distribution function F and finite mean μ∈R+,{N(n);n≥0} be a sequence of negative binomial distributed random variables with a parameter p ∈(0,1),n≥0,let {M(n);n≥0} be a Poisson process with intensity λ0.Suppose {N(n);n≥0},{Xn;n≥1} and {M(n);n≥0} are mutually results.These results can be applied to certain problems in insurance and finance.
Pooling overdispersed binomial data to estimate event rate
Directory of Open Access Journals (Sweden)
Chan K Arnold
2008-08-01
Full Text Available Abstract Background The beta-binomial model is one of the methods that can be used to validly combine event rates from overdispersed binomial data. Our objective is to provide a full description of this method and to update and broaden its applications in clinical and public health research. Methods We describe the statistical theories behind the beta-binomial model and the associated estimation methods. We supply information about statistical software that can provide beta-binomial estimations. Using a published example, we illustrate the application of the beta-binomial model when pooling overdispersed binomial data. Results In an example regarding the safety of oral antifungal treatments, we had 41 treatment arms with event rates varying from 0% to 13.89%. Using the beta-binomial model, we obtained a summary event rate of 3.44% with a standard error of 0.59%. The parameters of the beta-binomial model took the values of 1.24 for alpha and 34.73 for beta. Conclusion The beta-binomial model can provide a robust estimate for the summary event rate by pooling overdispersed binomial data from different studies. The explanation of the method and the demonstration of its applications should help researchers incorporate the beta-binomial method as they aggregate probabilities of events from heterogeneous studies.
James O Lloyd-Smith
2007-01-01
Background. The negative binomial distribution is used commonly throughout biology as a model for overdispersed count data, with attention focused on the negative binomial dispersion parameter, κ. A substantial literature exists on the estimation of κ, but most attention has focused on datasets that are not highly overdispersed (i.e., those with κ≥1), and the accuracy of confidence intervals estimated for κ is typically not explored. Methodology. This article presents a simulation study explo...
Lognormal and Gamma Mixed Negative Binomial Regression
Zhou, Mingyuan; Li, Lingbo; Dunson, David; Carin, Lawrence
2012-01-01
In regression analysis of counts, a lack of simple and efficient algorithms for posterior computation has made Bayesian approaches appear unattractive and thus underdeveloped. We propose a lognormal and gamma mixed negative binomial (NB) regression model for counts, and present efficient closed-form Bayesian inference; unlike conventional Poisson models, the proposed approach has two free parameters to include two different kinds of random effects, and allows the incorporation of prior inform...
Binomial menu auctions in government formation
Breitmoser, Yves
2011-01-01
In a menu auction, players submit bids for all choices the auctioneer A can make, and A then makes the choice that maximizes the sum of bids. In a binomial menu auction (BMA), players submit acceptance sets (indicating which choices they would support), and A chooses the option that maximizes his utility subject to acceptance of the respective players. Monetary transfers may be implicit, but players may also bid by offering "favors" and the like. BMAs provide a unified representation of both ...
Fractional differences and sums with binomial coefficients
Abdeljawad, Thabet; Baleanu, Dumitru; Jarad, Fahd; Agarwal, Ravi
2012-01-01
In fractional calculus there are two approaches to obtain fractional derivatives. The first approach is by iterating the integral and then defining a fractional order by using Cauchy formula to obtain Riemann fractional integrals and derivatives. The second approach is by iterating the derivative and then defining a fractional order by making use of the binomial theorem to obtain Gr\\"{u}nwald-Litnikov fractional derivatives. In this article we formulate the delta and nabla discrete versions f...
Multiplicity dependent and non-binomial efficiency corrections for particle number cumulants
Bzdak, Adam; Koch, Volker
2016-01-01
In this note we extend previous work on efficiency corrections for cumulant measurements [1,2]. We will discuss the limitations of the methods presented in these papers. Specifically we will consider multiplicity dependent efficiencies as well as a non-binomial efficiency distributions. We will discuss the most simple and straightforward methods to implement those corrections.
Binomial moment equations for stochastic reaction systems.
Barzel, Baruch; Biham, Ofer
2011-04-15
A highly efficient formulation of moment equations for stochastic reaction networks is introduced. It is based on a set of binomial moments that capture the combinatorics of the reaction processes. The resulting set of equations can be easily truncated to include moments up to any desired order. The number of equations is dramatically reduced compared to the master equation. This formulation enables the simulation of complex reaction networks, involving a large number of reactive species much beyond the feasibility limit of any existing method. It provides an equation-based paradigm to the analysis of stochastic networks, complementing the commonly used Monte Carlo simulations. PMID:21568538
A Note on Teaching Binomial Confidence Intervals
Santner, Thomas J.
1997-01-01
For constructing confidence intervals for a binomial proportion $p$, Simon (1996, Teaching Statistics) advocates teaching one of two large-sample alternatives to the usual $z$-intervals $\\hat{p} \\pm 1.96 \\times S.E(\\hat{p})$ where $S.E.(\\hat{p}) = \\sqrt{ \\hat{p} \\times (1 - \\hat{p})/n}$. His recommendation is based on the comparison of the closeness of the achieved coverage of each system of intervals to their nominal level. This teaching note shows that a different alternative to $z$-interv...
A Mechanistic Beta-Binomial Probability Model for mRNA Sequencing Data.
Smith, Gregory R; Birtwistle, Marc R
2016-01-01
A main application for mRNA sequencing (mRNAseq) is determining lists of differentially-expressed genes (DEGs) between two or more conditions. Several software packages exist to produce DEGs from mRNAseq data, but they typically yield different DEGs, sometimes markedly so. The underlying probability model used to describe mRNAseq data is central to deriving DEGs, and not surprisingly most softwares use different models and assumptions to analyze mRNAseq data. Here, we propose a mechanistic justification to model mRNAseq as a binomial process, with data from technical replicates given by a binomial distribution, and data from biological replicates well-described by a beta-binomial distribution. We demonstrate good agreement of this model with two large datasets. We show that an emergent feature of the beta-binomial distribution, given parameter regimes typical for mRNAseq experiments, is the well-known quadratic polynomial scaling of variance with the mean. The so-called dispersion parameter controls this scaling, and our analysis suggests that the dispersion parameter is a continually decreasing function of the mean, as opposed to current approaches that impose an asymptotic value to the dispersion parameter at moderate mean read counts. We show how this leads to current approaches overestimating variance for moderately to highly expressed genes, which inflates false negative rates. Describing mRNAseq data with a beta-binomial distribution thus may be preferred since its parameters are relatable to the mechanistic underpinnings of the technique and may improve the consistency of DEG analysis across softwares, particularly for moderately to highly expressed genes. PMID:27326762
A Mechanistic Beta-Binomial Probability Model for mRNA Sequencing Data.
Directory of Open Access Journals (Sweden)
Gregory R Smith
Full Text Available A main application for mRNA sequencing (mRNAseq is determining lists of differentially-expressed genes (DEGs between two or more conditions. Several software packages exist to produce DEGs from mRNAseq data, but they typically yield different DEGs, sometimes markedly so. The underlying probability model used to describe mRNAseq data is central to deriving DEGs, and not surprisingly most softwares use different models and assumptions to analyze mRNAseq data. Here, we propose a mechanistic justification to model mRNAseq as a binomial process, with data from technical replicates given by a binomial distribution, and data from biological replicates well-described by a beta-binomial distribution. We demonstrate good agreement of this model with two large datasets. We show that an emergent feature of the beta-binomial distribution, given parameter regimes typical for mRNAseq experiments, is the well-known quadratic polynomial scaling of variance with the mean. The so-called dispersion parameter controls this scaling, and our analysis suggests that the dispersion parameter is a continually decreasing function of the mean, as opposed to current approaches that impose an asymptotic value to the dispersion parameter at moderate mean read counts. We show how this leads to current approaches overestimating variance for moderately to highly expressed genes, which inflates false negative rates. Describing mRNAseq data with a beta-binomial distribution thus may be preferred since its parameters are relatable to the mechanistic underpinnings of the technique and may improve the consistency of DEG analysis across softwares, particularly for moderately to highly expressed genes.
NBLDA: Negative Binomial Linear Discriminant Analysis for RNA-Seq Data
Dong, Kai; Zhao, Hongyu; Wan, Xiang; Tong, Tiejun
2015-01-01
RNA-sequencing (RNA-Seq) has become a powerful technology to characterize gene expression profiles because it is more accurate and comprehensive than microarrays. Although statistical methods that have been developed for microarray data can be applied to RNA-Seq data, they are not ideal due to the discrete nature of RNA-Seq data. The Poisson distribution and negative binomial distribution are commonly used to model count data. Recently, Witten (2011) proposed a Poisson linear discriminant ana...
Marginalized zero-inflated negative binomial regression with application to dental caries.
Preisser, John S; Das, Kalyan; Long, D Leann; Divaris, Kimon
2016-05-10
The zero-inflated negative binomial regression model (ZINB) is often employed in diverse fields such as dentistry, health care utilization, highway safety, and medicine to examine relationships between exposures of interest and overdispersed count outcomes exhibiting many zeros. The regression coefficients of ZINB have latent class interpretations for a susceptible subpopulation at risk for the disease/condition under study with counts generated from a negative binomial distribution and for a non-susceptible subpopulation that provides only zero counts. The ZINB parameters, however, are not well-suited for estimating overall exposure effects, specifically, in quantifying the effect of an explanatory variable in the overall mixture population. In this paper, a marginalized zero-inflated negative binomial regression (MZINB) model for independent responses is proposed to model the population marginal mean count directly, providing straightforward inference for overall exposure effects based on maximum likelihood estimation. Through simulation studies, the finite sample performance of MZINB is compared with marginalized zero-inflated Poisson, Poisson, and negative binomial regression. The MZINB model is applied in the evaluation of a school-based fluoride mouthrinse program on dental caries in 677 children. PMID:26568034
Improving Convergence of Binomial Schemes and the Edgeworth Expansion
Directory of Open Access Journals (Sweden)
Alona Bock
2016-05-01
Full Text Available Binomial trees are very popular in both theory and applications of option pricing. As they often suffer from an irregular convergence behavior, improving this is an important task. We build upon a new version of the Edgeworth expansion for lattice models to construct new and quickly converging binomial schemes with a particular application to barrier options.
Penggunaan Model Binomial Pada Penentuan Harga Opsi Saham Karyawan
Directory of Open Access Journals (Sweden)
Dara Puspita Anggraeni
2015-11-01
Full Text Available Binomial Model for Valuing Employee Stock Options. Employee Stock Options (ESO differ from standard exchange-traded options. The three main differences in a valuation model for employee stock options : Vesting Period, Exit Rate and Non-Transferability. In this thesis, the model for valuing employee stock options discussed. This model are implement with a generalized binomial model.
Fractional Sums and Differences with Binomial Coefficients
Directory of Open Access Journals (Sweden)
Thabet Abdeljawad
2013-01-01
Full Text Available In fractional calculus, there are two approaches to obtain fractional derivatives. The first approach is by iterating the integral and then defining a fractional order by using Cauchy formula to obtain Riemann fractional integrals and derivatives. The second approach is by iterating the derivative and then defining a fractional order by making use of the binomial theorem to obtain Grünwald-Letnikov fractional derivatives. In this paper we formulate the delta and nabla discrete versions for left and right fractional integrals and derivatives representing the second approach. Then, we use the discrete version of the Q-operator and some discrete fractional dual identities to prove that the presented fractional differences and sums coincide with the discrete Riemann ones describing the first approach.
David Shilane; Derek Bean
2013-01-01
The negative binomial distribution becomes highly skewed under extreme dispersion. Even at moderately large sample sizes, the sample mean exhibits a heavy right tail. The standard normal approximation often does not provide adequate inferences about the data's expected value in this setting. In previous work, we have examined alternative methods of generating confidence intervals for the expected value. These methods were based upon Gamma and Chi Square approximations or tail probability boun...
Beta-Negative Binomial Process and Exchangeable Random Partitions for Mixed-Membership Modeling
Zhou, Mingyuan
2014-01-01
The beta-negative binomial process (BNBP), an integer-valued stochastic process, is employed to partition a count vector into a latent random count matrix. As the marginal probability distribution of the BNBP that governs the exchangeable random partitions of grouped data has not yet been developed, current inference for the BNBP has to truncate the number of atoms of the beta process. This paper introduces an exchangeable partition probability function to explicitly describe how the BNBP clu...
Bhattacharya, Kaushik
2010-01-01
The paper specifies a model of the first-past-the-post (FPTP) electoral system in which political parties themselves float independent candidates to gain electoral advantage, leading to a Prisoners’ Dilemma type game where each party tries to out-maneuver one another. Imposing some intuitively appealing assumptions on this game, we show that the total number of independent candidates across constituencies would follow a Negative Binomial distribution. Empirical results for the 2004 parliament...
Bayesian Estimation of Negative Binomial Parameters with Applications to RNA-Seq Data
Leon-Novelo, Luis; Claudio FUENTES; Emerson, Sarah
2015-01-01
RNA-Seq data characteristically exhibits large variances, which need to be appropriately accounted for in the model. We first explore the effects of this variability on the maximum likelihood estimator (MLE) of the overdispersion parameter of the negative binomial distribution, and propose instead the use an estimator obtained via maximization of the marginal likelihood in a conjugate Bayesian framework. We show, via simulation studies, that the marginal MLE can better control this variation ...
The destructive negative binomial cure rate model with a latent activation scheme
Cancho, Vicente G.; Bandyopadhyay, Dipankar; Louzada, Francisco; Yiqi, Bao
2013-01-01
A new flexible cure rate survival model is developed where the initial number of competing causes of the event of interest (say lesions or altered cells) follow a compound negative binomial (NB) distribution. This model provides a realistic interpretation of the biological mechanism of the event of interest as it models a destructive process of the initial competing risk factors and records only the damaged portion of the original number of risk factors. Besides, it also acc...
Empat Model Aproksimasi Binomial Harga Saham Model black-Scholes
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Abdul Aziz
2009-11-01
Full Text Available Kami akan menyajikan empat bentuk nilai parameter-parameter u, d, dan p dalam model Binomial harga saham, yang dihasilkan dengan menggunakan penyamaan ekspektasi dan variansi model diskrit dengan kontinu. Metode pertama menggunakan asumsi u . d = 1, yang mana metode ini dapat menghasilkan tiga bentuk solusi untuk parameter-parameter u, d, dan p dalam model Binomial harga saham. Metode kedua menggunakan asumsi p = 0,5. Dari kedua metode ini ternyata dapat dihasilkan empat bentuk solusi u, d, dan p yang berbeda dan akan dibandingkan hasilnya dalam pendekatan nilai option dalam model Binomial dengan model Black-Scholes.
Parameter Estimation Based on the Frèchet Progressive Type II Censored Data with Binomial Removals
Directory of Open Access Journals (Sweden)
Mohamed Mubarak
2012-01-01
Full Text Available This paper considers the estimation problem for the Frèchet distribution under progressive Type II censoring with random removals, where the number of units removed at each failure time has a binomial distribution. We use the maximum likelihood method to obtain the estimators of parameters and derive the sampling distributions of the estimators, and we also construct the confidence intervals for the parameters and percentile of the failure time distribution.
Kanthamanond, Piti
2009-01-01
The fuzzy set concept can be applied to the derivative pricing model to cover the uncertainty in the market. The aim of this study is to modify existing fuzzy binomial option pricing models and tests them with several lattice numerical methods to compare the performance and clarify the benefit and necessity of the fuzzy models over the non-fuzzy models. The empirical validation of these models on the artificial data and on the S&P 100 index options is provided with the various tests which cov...
Application of binomial-edited CPMG to shale characterization
Washburn, Kathryn E.; Birdwell, Justin E.
2014-01-01
Unconventional shale resources may contain a significant amount of hydrogen in organic solids such as kerogen, but it is not possible to directly detect these solids with many NMR systems. Binomial-edited pulse sequences capitalize on magnetization transfer between solids, semi-solids, and liquids to provide an indirect method of detecting solid organic materials in shales. When the organic solids can be directly measured, binomial-editing helps distinguish between different phases. We applied a binomial-edited CPMG pulse sequence to a range of natural and experimentally-altered shale samples. The most substantial signal loss is seen in shales rich in organic solids while fluids associated with inorganic pores seem essentially unaffected. This suggests that binomial-editing is a potential method for determining fluid locations, solid organic content, and kerogen–bitumen discrimination.
Randomized Binomial Tree and Pricing of American-Style Options
Directory of Open Access Journals (Sweden)
Hu Xiaoping
2014-01-01
Full Text Available Randomized binomial tree and methods for pricing American options were studied. Firstly, both the completeness and the no-arbitrage conditions in the randomized binomial tree market were proved. Secondly, the description of the node was given, and the cubic polynomial relationship between the number of nodes and the time steps was also obtained. Then, the characteristics of paths and storage structure of the randomized binomial tree were depicted. Then, the procedure and method for pricing American-style options were given in a random binomial tree market. Finally, a numerical example pricing the American option was illustrated, and the sensitivity analysis of parameter was carried out. The results show that the impact of the occurrence probability of the random binomial tree environment on American option prices is very significant. With the traditional complete market characteristics of random binary and a stronger ability to describe, at the same time, maintaining a computational feasibility, randomized binomial tree is a kind of promising method for pricing financial derivatives.
López Martínez, Laura Elizabeth
2010-01-01
En este trabajo se realiza inferencia estadística en la distribución Binomial Negativa Generalizada (BNG) y los modelos que anida, los cuales son Binomial, Binomial Negativa y Poisson. Se aborda el problema de estimación de parámetros en la distribución BNG y se propone una prueba de razón de verosimilitud generalizada para discernir si un conjunto de datos se ajusta en particular al modelo Binomial, Binomial Negativa o Poisson. Además, se estudian las potencias y tamaños de la prueba p...
Renormdynamics, multiparticle production, negative binomial distribution, and Riemann zeta function
Makhaldiani, N. V.
2013-09-01
After short introduction, we consider different aspects of the renormdynamics. Then scaling functions of the multiparticle production processes and corresponding stochastic dynamics are considered. Nonperturbative quasi-particle dynamics is considered on the base of the toy QCD- O( N)-sigma model. Last section concerns to the NBD-Riemann zeta function connection.
Renormdynamics, multiparticle production, negative binomial distribution, and Riemann zeta function
Energy Technology Data Exchange (ETDEWEB)
Makhaldiani, N. V., E-mail: mnv@jinr.ru [Joint Institute for Nuclear Research (Russian Federation)
2013-09-15
After short introduction, we consider different aspects of the renormdynamics. Then scaling functions of the multiparticle production processes and corresponding stochastic dynamics are considered. Nonperturbative quasi-particle dynamics is considered on the base of the toy QCD-O(N)-sigma model. Last section concerns to the NBD-Riemann zeta function connection.
QUANTUM THEORY FOR THE BINOMIAL MODEL IN FINANCE THEORY
Institute of Scientific and Technical Information of China (English)
CHEN Zeqian
2004-01-01
In this paper, a quantum model for the binomial market in finance is proposed. We show that its risk-neutral world exhibits an intriguing structure as a disk in the unit ball of R3, whose radius is a function of the risk-free interest rate with two thresholds which prevent arbitrage opportunities from this quantum market. Furthermore, from the quantum mechanical point of view we re-deduce the Cox-Ross-Rubinstein binomial option pricing formula by considering Maxwell-Boltzmann statistics of the system of N distinguishable particles.
Properties of some test of equality of two negative binomial samples
Hübnerová, Zuzana; Doudová, Lucie
2013-10-01
When comparing two independent samples from the negative binomial distribution the test of equality of their expected values might be of interest. In this case, the assumptions on the nuisance shape parameter determine the form of suitable test statistic. This paper focuses on test based on Wald statistic under an assumption that the shape parameters in the two samples are known and equal. However, the common shape parameter might be replaced by its estimate, either statistical or expert. We discuss the consequences of this procedure on the power as well as on the size of the test (probability of rejection of H0 when it is true).
A binomial stochastic kinetic approach to the Michaelis-Menten mechanism
Lente, Gábor
2013-05-01
This Letter presents a new method that gives an analytical approximation of the exact solution of the stochastic Michaelis-Menten mechanism without computationally demanding matrix operations. The method is based on solving the deterministic rate equations and then using the results as guiding variables of calculating probability values using binomial distributions. This principle can be generalized to a number of different kinetic schemes and is expected to be very useful in the evaluation of measurements focusing on the catalytic activity of one or a few individual enzyme molecules.
Selecting the highest probability in binomial or multinomial trials
Levin, Bruce; Robbins, Herbert
1981-01-01
Some sequential procedures are considered for selecting the binomial population with largest success probability or for selecting the multinomial outcome with highest cell probability. Procedures with and without sequential elimination of inferior populations are evaluated with respect to the expected probability of the population selected.
Iterated binomial sums and their associated iterated intergrals
Energy Technology Data Exchange (ETDEWEB)
Ablinger, J.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, J.; Raab, C.G. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2014-06-15
We consider finite iterated generalized harmonic sums weighted by the binomial ({sup 2k}{sub k}) in numerators and denominators. A large class of these functions emerges in the calculation of massive Feynman diagrams with local operator insertions starting at 3-loop order in the coupling constant and extends the classes of the nested harmonic, generalized harmonic and cyclotomic sums. The binomially weighted sums are associated by the Mellin transform to iterated integrals over square-root valued alphabets. The values of the sums for N→∞ and the iterated integrals at x=1 lead to new constants, extending the set of special numbers given by the multiple zeta values, the cyclotomic zeta values and special constants which emerge in the limit N→∞ of generalized harmonic sums. We develop algorithms to obtain the Mellin representations of these sums in a systematic way. They are of importance for the derivation of the asymptotic expansion of these sums and their analytic continuation to N element of C. The associated convolution relations are derived for real parameters and can therefore be used in a wider context, as e.g. for multi-scale processes. We also derive algorithms to transform iterated integrals over root-valued alphabets into binomial sums. Using generating functions we study a few aspects of infinite (inverse) binomial sums.
Using Binomial Tree Pricing Model in a Fuzzy Market
Institute of Scientific and Technical Information of China (English)
YOU Su-rong; LU Yun-sheng
2007-01-01
A model of using binomial tree pricing formulae in a fuzzy market is proposed. In the fuzzy market, a price interval can be got according to the belief degree. The rule for the reasonability of the price interval is proposed. The explicit expression of the interval is discussed in some special settings.
Iterated binomial sums and their associated iterated intergrals
International Nuclear Information System (INIS)
We consider finite iterated generalized harmonic sums weighted by the binomial (2kk) in numerators and denominators. A large class of these functions emerges in the calculation of massive Feynman diagrams with local operator insertions starting at 3-loop order in the coupling constant and extends the classes of the nested harmonic, generalized harmonic and cyclotomic sums. The binomially weighted sums are associated by the Mellin transform to iterated integrals over square-root valued alphabets. The values of the sums for N→∞ and the iterated integrals at x=1 lead to new constants, extending the set of special numbers given by the multiple zeta values, the cyclotomic zeta values and special constants which emerge in the limit N→∞ of generalized harmonic sums. We develop algorithms to obtain the Mellin representations of these sums in a systematic way. They are of importance for the derivation of the asymptotic expansion of these sums and their analytic continuation to N element of C. The associated convolution relations are derived for real parameters and can therefore be used in a wider context, as e.g. for multi-scale processes. We also derive algorithms to transform iterated integrals over root-valued alphabets into binomial sums. Using generating functions we study a few aspects of infinite (inverse) binomial sums.
Computer generation of initial spatial distribution for cell automata
GuangHua Liu; WenJun Zhang
2011-01-01
The algorithm to generate spatial distribution patterns was developed and presented in this study. Three typical spatial distribution patterns, i.e., Poisson distribution, binomial distribution, and negative binomial distribution were included in the algorithm. The Java program was also provided. The algorithm can be used to generate initial distribution in cell automata modeling.
Blanco, Rocio
2009-01-01
This paper is devoted to give all the technical constructions and definitions that will lead to the construction of an algorithm of resolution of singularities for binomial ideals. We construct a resolution function that will provide a resolution of singularities for binomial ideals, over a field of arbitrary characteristic. For us, a binomial ideal means an ideal generated by binomial equations without any restriction, including monomials and $p$-th powers, where $p$ is the characteristic of...
Comparing of the binomial model and the black-scholes model for options pricing
Lazarova, Limonka; Jolevska-Tuneska, Biljana; Atanasova-Pacemska, Tatjana
2014-01-01
In this paper will be considered the simple binomial model with one and more periods. It will be given the correspondence between binomial model and the Black-Scholes model for option pricing and also will be shown that the binomial model is more simple then the continuous Black- Scholes model from pedagogical point of view.
Institute of Scientific and Technical Information of China (English)
周杰明; 莫晓云; 欧辉; 杨向群
2013-01-01
In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. The premium income is assumed to another binomial process to capture the uncertainty of the customer’s arrivals and payments. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are Kn distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.
Jie Q. Guo; Tong Li
2001-01-01
This paper studies the effects and estimation of errors-in-variables negative binomial regression model. We prove that in the presence of measurement errors, in general, maximum likelihood estimator of the overdispersion using the observed data is biased upward. We adopt a structural approach assuming that the distribution of the latent variables is known and propose a simulation-based corrected maximum likelihood estimator and a simulation-based corrected score estimator to estimate the erro...
Nakajima, Tetsuo
2008-11-01
The recursion formulas for the photon paths in the Borrmann triangle, which satisfy a new modified Pascal triangle can be derived from the binomial theorem by regarding the permutation of the stochastic variables of the diffracted and transmitted X-ray photons. The Borrmann triangle for the n-multiple X-ray reflections expanded by the n-degree binomial distribution consists of the two sub-triangles given by the ( n-1)-degree binomial distribution of the diffracted and transmitted photons. The former sub-triangle shows perfectly flawless symmetry but the latter one shows inevitable asymmetry. A reasonable understanding of both the high intense and very weak photon flows in the Borrmann triangle, which are popularly known as the anomalous transmission and absorption, respectively, are derived from the binomial theorem. Incident photons irradiated at a point O that forms the vertex of the Borrmann triangle propagate through the bypasses parallel to only the complementary half of the integral whole median with the high probabilities from the binomial theorem and emanate them from a short width slit of overline{O'O''} on the base of the high intense photon flow Borrmann triangle ▵ OO' O″, which can be defined by the standard deviation of the normal distribution. The parallel paths to the whole median also pass the very weak photon flows from the high power exponent of d multinomials through the triangle ▵ OO' O″. Both the above contrastive photon flows could coexist in ▵ OO' O″ based upon the complementary rivalry duality from the binomial theorem of ( d+ t) n =1, including the very weak photon flows from the high power exponent of t multinomials near both sides of the Borrmann triangle.
Binomial Approximations for Barrier Options of Israeli Style
Dolinsky, Yan
2009-01-01
We show that prices and shortfall risks of game (Israeli) barrier options in a sequence of binomial approximations of the Black--Scholes (BS) market converge to the corresponding quantities for similar game barrier options in the BS market with path dependent payoffs and the speed of convergence is estimated, as well. The results are new also for usual American style options and they are interesting from the computational point of view, as well, since in binomial markets these quantities can be obtained via dynamical programming algorithms. The paper continues the study of [11]and [7] but requires substantial additional arguments in view of pecularities of barrier options which, in particular, destroy the regularity of payoffs needed in the above papers.
On pricing futures options on random binomial tree
International Nuclear Information System (INIS)
The discrete-time approach to real option valuation has typically been implemented in the finance literature using a binomial tree framework. Instead we develop a new model by randomizing the environment and call such model a random binomial tree. Whereas the usual model has only one environment (u, d) where the price of underlying asset can move by u times up and d times down, and pair (u, d) is constant over the life of the underlying asset, in our new model the underlying security is moving in two environments namely (u1, d1) and (u2, d2). Thus we obtain two volatilities σ1 and σ2. This new approach enables calculations reflecting the real market since it consider the two states of market normal and extra ordinal. In this paper we define and study Futures options for such models.
Central Binomial Sums, Multiple Clausen Values and Zeta Values
Borwein, J M; Kamnitzer, J
2000-01-01
We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Ap\\'ery sums). The study of non-alternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ratio. In the non-alternating case, there is a strong connection to polylogarithms of the sixth root of unity, encountered in the 3-loop Feynman diagrams of {\\tt hep-th/9803091} and subsequently in hep-ph/9910223, hep-ph/9910224, cond-mat/9911452 and hep-th/0004010.
Determination of finite-difference weights using scaled binomial windows
Chu, Chunlei
2012-05-01
The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties. © 2012 Society of Exploration Geophysicists.
Generalized binomial transform applied to the divergent series
Yamada, Hirofumi
2015-01-01
The divergent series for a function defined through Lapalce integral and the ground state energy of the quartic anharmonic oscillator to large orders are studied to test the generalized binomial transform which is the renamed version of $\\delta$-expansion proposed recently. We show that, by the use of the generalized binomial transform, the values of functions in the limit of zero of an argument is approximately computable from the series expansion around the infinity of the same argument. In the Laplace integral, we investigate the subject in detail with the aid of Mellin transform. In the anharmonic oscillator, we compute the strong coupling limit of the ground state energy and also the expansion coefficients at strong coupling from the weak coupling perturbation series. The obtained result is compared with that of the linear delta expansion.
Comparing the Convergence Behaviour of Binomial and Trinomial Models
Mehmet Horasanli
2007-01-01
An American option differs from a European one by the early exercise possibility. An American option can be exercised at any time up to the maturity date. In general, there is unfortunately no analytical solution to the American option problem. Binomial and trinomial approximations are useful to solve this problem but using a lattice model introduces approximation error. Both models have the property of convergence to Black & Scholes prices thus; can be used alternatively to solve the Black &...
Comparing the Convergence Behaviour of Binomial and Trinomial Models
Mehmet Horasanli
2008-01-01
An American option differs from a European one by the early exercise possibility. An American option can be exercised at any time up to the maturity date. In general, there is unfortunately no analytical solution to the American option problem. Binomial and trinomial approximations are useful to solve this problem but using a lattice model introduces approximation error. Both models have the property of convergence to Black & Scholes prices thus; can be used alternatively to solve the Black &...
On the least common multiple of $q$-binomial coefficients
Guo, Victor J. W.
2009-01-01
In this paper, we prove the following identity $$ \\lcm({n\\brack 0}_q,{n\\brack 1}_q,...,{n\\brack n}_q) =\\frac{\\lcm([1]_q,[2]_q,...,[n+1]_q)}{[n+1]_q}, $$ where ${n\\brack k}_q$ denotes the $q$-binomial coefficient and $[n]_q=\\frac{1-q^n}{1-q}$. This result is a $q$-analogue of an identity of Farhi [Amer. Math. Monthly, November (2009)].
The combinatorial structure of beta negative binomial processes
Heaukulani, Creighton; Roy, Daniel M.
2013-01-01
We characterize the combinatorial structure of conditionally-i.i.d. sequences of negative binomial processes with a common beta process base measure. In Bayesian nonparametric applications, such processes have served as models for latent multisets of features underlying data. Analogously, random subsets arise from conditionally-i.i.d. sequences of Bernoulli processes with a common beta process base measure, in which case the combinatorial structure is described by the Indian buffet process. O...
Hits per trial: Basic analysis of binomial data
International Nuclear Information System (INIS)
This report presents simple statistical methods for analyzing binomial data, such as the number of failures in some number of demands. It gives point estimates, confidence intervals, and Bayesian intervals for the failure probability. It shows how to compare subsets of the data, both graphically and by statistical tests, and how to look for trends in time. It presents a compound model when the failure probability varies randomly. Examples and SAS programs are given
Beta-Negative Binomial Process and Poisson Factor Analysis
Zhou, Mingyuan; Hannah, Lauren; Dunson, David; Carin, Lawrence
2011-01-01
A beta-negative binomial (BNB) process is proposed, leading to a beta-gamma-Poisson process, which may be viewed as a "multi-scoop" generalization of the beta-Bernoulli process. The BNB process is augmented into a beta-gamma-gamma-Poisson hierarchical structure, and applied as a nonparametric Bayesian prior for an infinite Poisson factor analysis model. A finite approximation for the beta process Levy random measure is constructed for convenient implementation. Efficient MCMC computations are...
Influences on leadership behaviour: a binomial logit model
Titus Oshagbemi; Samuel A. Ocholi
2013-01-01
Purpose – The purpose of this article is to review what influences leaders' behaviours and why leaders behave in certain ways and not in other ways. Using a range of job characteristics such as the different leadership styles utilised in conducting various tasks and the leaders' age and gender for example, and employing a binomial logit analysis on a survey data, this research focuses on a range of possible influences on leadership behaviours. Design/methodology/approach – To investigate the ...
Constructions for a bivariate beta distribution
Olkin, Ingram; Trikalinos, Thomas A.
2014-01-01
The beta distribution is a basic distribution serving several purposes. It is used to model data, and also, as a more flexible version of the uniform distribution, it serves as a prior distribution for a binomial probability. The bivariate beta distribution plays a similar role for two probabilities that have a bivariate binomial distribution. We provide a new multivariate distribution with beta marginal distributions, positive probability over the unit square, and correlations over the full ...
Moghimbeigi, Abbas
2015-05-01
Poisson regression models provide a standard framework for quantitative trait locus (QTL) mapping of count traits. In practice, however, count traits are often over-dispersed relative to the Poisson distribution. In these situations, the zero-inflated Poisson (ZIP), zero-inflated generalized Poisson (ZIGP) and zero-inflated negative binomial (ZINB) regression may be useful for QTL mapping of count traits. Added genetic variables to the negative binomial part equation, may also affect extra zero data. In this study, to overcome these challenges, I apply two-part ZINB model. The EM algorithm with Newton-Raphson method in the M-step uses for estimating parameters. An application of the two-part ZINB model for QTL mapping is considered to detect associations between the formation of gallstone and the genotype of markers. PMID:25728790
Directory of Open Access Journals (Sweden)
James O Lloyd-Smith
Full Text Available BACKGROUND: The negative binomial distribution is used commonly throughout biology as a model for overdispersed count data, with attention focused on the negative binomial dispersion parameter, k. A substantial literature exists on the estimation of k, but most attention has focused on datasets that are not highly overdispersed (i.e., those with k>or=1, and the accuracy of confidence intervals estimated for k is typically not explored. METHODOLOGY: This article presents a simulation study exploring the bias, precision, and confidence interval coverage of maximum-likelihood estimates of k from highly overdispersed distributions. In addition to exploring small-sample bias on negative binomial estimates, the study addresses estimation from datasets influenced by two types of event under-counting, and from disease transmission data subject to selection bias for successful outbreaks. CONCLUSIONS: Results show that maximum likelihood estimates of k can be biased upward by small sample size or under-reporting of zero-class events, but are not biased downward by any of the factors considered. Confidence intervals estimated from the asymptotic sampling variance tend to exhibit coverage below the nominal level, with overestimates of k comprising the great majority of coverage errors. Estimation from outbreak datasets does not increase the bias of k estimates, but can add significant upward bias to estimates of the mean. Because k varies inversely with the degree of overdispersion, these findings show that overestimation of the degree of overdispersion is very rare for these datasets.
Directory of Open Access Journals (Sweden)
David Shilane
2013-01-01
Full Text Available The negative binomial distribution becomes highly skewed under extreme dispersion. Even at moderately large sample sizes, the sample mean exhibits a heavy right tail. The standard normal approximation often does not provide adequate inferences about the data's expected value in this setting. In previous work, we have examined alternative methods of generating confidence intervals for the expected value. These methods were based upon Gamma and Chi Square approximations or tail probability bounds such as Bernstein's inequality. We now propose growth estimators of the negative binomial mean. Under high dispersion, zero values are likely to be overrepresented in the data. A growth estimator constructs a normal-style confidence interval by effectively removing a small, predetermined number of zeros from the data. We propose growth estimators based upon multiplicative adjustments of the sample mean and direct removal of zeros from the sample. These methods do not require estimating the nuisance dispersion parameter. We will demonstrate that the growth estimators' confidence intervals provide improved coverage over a wide range of parameter values and asymptotically converge to the sample mean. Interestingly, the proposed methods succeed despite adding both bias and variance to the normal approximation.
On Some Distributions Arising in Inverse Cluster Sampling
Xekalaki, Evdokia; Panaretos, John
1989-01-01
In this paper, distributions of items sampled inversely in clusters are derived. In particular, negative binomial type of distributions are obtained and their properties are studied. A logarithmic series, type of distribution is also defined as limiting form of the obtained generalized negative binomial distribution
Interval Estimation for Binomial Proportion, Poisson Mean, and Negative –binomial Mean
Liu, Luchen
2012-01-01
This paper studies the interval estimation of three discrete distributions: thebinomial distribution, the Poisson distribution and the negative-binomialdistribution. The problem is the chaotic behavior of the coverage probabilityfor the Wald interval. To solve this problem, alternative confidence intervals areintroduced. Coverage probability and expected length are chosen to be thecriteria evaluating the intervals.In this paper, I firstly tested the chaotic behavior of the coverageprobability...
Generalized distributions of order k associated with success runs in Bernoulli trials
Gregory A. Tripsiannis; Papathanasiou, Afroditi A.; Philippou, Andreas N.
2003-01-01
In a sequence of independent Bernoulli trials, by counting multidimensional lattice paths in order to compute the probability of a first-passage event, we derive and study a generalized negative binomial distribution of order k, type I, which extends to distributions of order k, the generalized negative binomial distribution of Jain and Consul (1971), and includes as a special case the negative binomial distribution of order k, type I, of Philippou et al. (1983). This new distribution gives r...
Estimators for the binomial failure rate common cause model
International Nuclear Information System (INIS)
In Vesely's binomial failure rate model, a system of m components is hit by random shocks which may cause components simultaneously to fail, each component equal probability. Individual components may also fail when no shock has occurred. The data possibilities considered are that caused of single failures are identifiable (as shock or not) or not identifiable. Given data from such a system, non-Bayesian and Bayesian point and interval estimators are found for the various quantities of interest. Residual analyses and hypothesis tests are presented for checking the model assumptions. An example is worked out
The binomial edge ideal of a pair of graphs
Ene, Viviana; Hibi, Takayuki; Qureshi, Ayesha Asloob
2012-01-01
We introduce a class of ideals generated by a set of 2-minors of $m\\times n$-matrix of indeterminates indexed by a pair of graphs. This class of ideals is a natural common generalization of binomial edge ideals and ideals generated by adjacent minors. We determine the minimal prime ideals of such ideals and give a lower bound for their degree of nilpotency. In some special cases we compute their Gr\\"obner basis and characterize unmixedness and Cohen--Macaulayness.
Directory of Open Access Journals (Sweden)
Manoj Kumar
2016-03-01
Full Text Available In this paper, a poissoin-exponential distribution(PED is considered as a lifetime model. Its statistical characteristics and important distributional properties are discussed by Louzada-Neto et al.[13]. The method of Maximum likelihood estimation and least square estimation of parameters involved along with reliability and failure rate functions is also studied here. In view of cost and time constraints, Progressive type-II censored data with binomial removals (PT-II CBRs have been used. Finally, a real data example is given to show the practical applications of the paper.
THE INTERLINGUAL ERRORS OF ARAB STUDENTS IN THE USE OF ENGLISH BINOMIALS
Mohamed, Abdul minam Mahmod [عبد المنعم محمود محمد
2003-01-01
This study focuses on the interlingual errors made by adult Arab learners in the use of the English binomials. Thus, it adds one more area to those where language transfer has been reported. A total of 73 binomials were collected from the oral and written presentation of the second year university students majoring in English. The incorrect binomials (85%) could all be attributed to negative transfer from Arabic. These were grouped and analyzed under three main categories: grammatical errors,...
Directory of Open Access Journals (Sweden)
Xiong Wang
2013-01-01
Full Text Available Based on characteristics of the nonlife joint-stock insurance company, this paper presents a compound binomial risk model that randomizes the premium income on unit time and sets the threshold for paying dividends to shareholders. In this model, the insurance company obtains the insurance policy in unit time with probability and pays dividends to shareholders with probability when the surplus is no less than . We then derive the recursive formulas of the expected discounted penalty function and the asymptotic estimate for it. And we will derive the recursive formulas and asymptotic estimates for the ruin probability and the distribution function of the deficit at ruin. The numerical examples have been shown to illustrate the accuracy of the asymptotic estimations.
Estimation of adjusted rate differences using additive negative binomial regression.
Donoghoe, Mark W; Marschner, Ian C
2016-08-15
Rate differences are an important effect measure in biostatistics and provide an alternative perspective to rate ratios. When the data are event counts observed during an exposure period, adjusted rate differences may be estimated using an identity-link Poisson generalised linear model, also known as additive Poisson regression. A problem with this approach is that the assumption of equality of mean and variance rarely holds in real data, which often show overdispersion. An additive negative binomial model is the natural alternative to account for this; however, standard model-fitting methods are often unable to cope with the constrained parameter space arising from the non-negativity restrictions of the additive model. In this paper, we propose a novel solution to this problem using a variant of the expectation-conditional maximisation-either algorithm. Our method provides a reliable way to fit an additive negative binomial regression model and also permits flexible generalisations using semi-parametric regression functions. We illustrate the method using a placebo-controlled clinical trial of fenofibrate treatment in patients with type II diabetes, where the outcome is the number of laser therapy courses administered to treat diabetic retinopathy. An R package is available that implements the proposed method. Copyright © 2016 John Wiley & Sons, Ltd. PMID:27073156
A Generic Multivariate Distribution for Counting Data
Capistrán, Marcos; Christen, J. Andrés
2011-01-01
Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete distribution. Based on blending the Binomial, Poisson and Negative-Binomial distributions, and using a normal multivariate copula, the required distribution is defined. This distribution tends to the Multivariate Normal for large counts and has an approximate pmf versi...
Weak convergence to the t-distribution
Christian Schluter; Mark Trede
2011-01-01
We present a new limit theorem for random means: if the sample size is not deterministic but has a negative binomial or geometric distribution, the limit distribution of the normalised random mean is a t-distribution with degrees of freedom depending on the shape parameter of the negative binomial distribution. Thus the limit distribution exhibits exhibits heavy tails, whereas limit laws for random sums do not achieve this unless the summands have in nite variance. The limit law may help expl...
Adjusted Wald Confidence Interval for a Difference of Binomial Proportions Based on Paired Data
Bonett, Douglas G.; Price, Robert M.
2012-01-01
Adjusted Wald intervals for binomial proportions in one-sample and two-sample designs have been shown to perform about as well as the best available methods. The adjusted Wald intervals are easy to compute and have been incorporated into introductory statistics courses. An adjusted Wald interval for paired binomial proportions is proposed here and…
On sums involving products of three binomial coefficients
Sun, Zhi-Wei
2010-01-01
In this paper we mainly employ the Zeilberger algorithm to study congruences for sums of terms involving products of three binomial coefficients. Let $p>3$ be a prime. We prove that $$\\sum_{k=0}^{p-1}\\frac{\\binom{2k}k^2\\binom{2k}{k+d}}{64^k}\\equiv 0\\pmod{p^2}$$ for all $d\\in\\{0,\\ldots,p-1\\}$ with $d\\equiv (p+1)/2\\pmod2$. If $p\\equiv 1\\pmod4$ and $p=x^2+y^2$ with $x\\equiv 1\\pmod4$ and $y\\equiv 0\\pmod2$, then we show $$\\sum_{k=0}^{p-1}\\frac{\\binom{2k}k^2\\binom{2k}{k+1}}{(-8)^k}\\equiv 2p-2x^2\\pm...
Probabilidades de ruína e o modelo binomial
Jerónimo, Isabel Brandão
2004-01-01
Mestrado em Ciências Actuariais Nesta dissertação, vamos apresentar o modelo binomial composto em tempo discreto e calcular probabilidades de ruína. Do ponto de vista da probabilidade de ruína em tempo finito, em vez de ter em linha de conta o instante temporal em que a ruína ocorre, estudamos a probabilidade da ruína ocorrer na n-ésima indemnizacão e o número de indem¬nizações ocorridas durante o período de recuperação do processo de risco. O nosso objectivo e, não só, obter resultados nu...
Calculation Methods for Wallenius’ Noncentral Hypergeometric Distribution
DEFF Research Database (Denmark)
Fog, Agner
2008-01-01
conditional distribution of independent binomial variates given their sum. No reliable calculation method for Wallenius' noncentral hypergeometric distribution has hitherto been described in the literature. Several new methods for calculating probabilities from Wallenius' noncentral hypergeometric...
Institute of Scientific and Technical Information of China (English)
WANG XiaoGuang; FU Hong-Chen
2001-01-01
We introduce new kinds of states of quantized radiation fields, which are the superpositions of negative binomial states. They exhibit remarkable nonclassical properties and reduce to Schrodinger cat states in a certain limit.The algebras involved in the even and odd negative binomial states turn out to be generally deformed oscillator algebras.It is found that the even and odd negative binomial states satisfy the same eigenvalue equation with the same eigenvalue and they can be viewed as two-photon nonlinear coherent states. Two methods of generating such the states are proposed.``
Low reheating temperatures in monomial and binomial inflationary potentials
Rehagen, Thomas
2015-01-01
We investigate the allowed range of reheating temperature values in light of the Planck 2015 results and the recent joint analysis of Cosmic Microwave Background (CMB) data from the BICEP2/Keck Array and Planck experiments, using monomial and binomial inflationary potentials. While the well studied $\\phi^2$ inflationary potential is no longer favored by current CMB data, as well as $\\phi^p$ with $p>2$, a $\\phi^1$ potential and canonical reheating ($w_{re}=0$) provide a good fit to the CMB measurements. In this last case, we find that the Planck 2015 $68\\%$ confidence limit upper bound on the spectral index, $n_s$, implies an upper bound on the reheating temperature of $T_{re}\\lesssim 6\\times 10^{10}\\,{\\rm GeV}$, and excludes instantaneous reheating. The low reheating temperatures allowed by this model open the possiblity that dark matter could be produced during the reheating period instead of when the Universe is radiation dominated, which could lead to very different predictions for the relic density and mo...
Microbial comparative pan-genomics using binomial mixture models
Directory of Open Access Journals (Sweden)
Ussery David W
2009-08-01
Full Text Available Abstract Background The size of the core- and pan-genome of bacterial species is a topic of increasing interest due to the growing number of sequenced prokaryote genomes, many from the same species. Attempts to estimate these quantities have been made, using regression methods or mixture models. We extend the latter approach by using statistical ideas developed for capture-recapture problems in ecology and epidemiology. Results We estimate core- and pan-genome sizes for 16 different bacterial species. The results reveal a complex dependency structure for most species, manifested as heterogeneous detection probabilities. Estimated pan-genome sizes range from small (around 2600 gene families in Buchnera aphidicola to large (around 43000 gene families in Escherichia coli. Results for Echerichia coli show that as more data become available, a larger diversity is estimated, indicating an extensive pool of rarely occurring genes in the population. Conclusion Analyzing pan-genomics data with binomial mixture models is a way to handle dependencies between genomes, which we find is always present. A bottleneck in the estimation procedure is the annotation of rarely occurring genes.
On Moran's Property of the Poisson Distribution
Panaretos, John
1983-01-01
Two interesting results encountered in the literature concerning the Poisson and the negative binomial distributions are due to MORAN (1952) and PATIL & SESHADRI (1964), respectively. MORAN's result provided a fundamental property of the Poisson distribution. Roughly speaking, he has shown that if Y, Z are independent, non-negative, integer-valued random variables with X=Y | Z then, under some mild restrictions, the conditional distribution of Y | X is binomial if and only if Y, Z are Poi...
Directory of Open Access Journals (Sweden)
Hugo Alvarado Martínez
2010-12-01
Full Text Available En este trabajo se describe un proceso de reflexión sobre la enseñanza de la estadística a nivel universitario. Para ello se analiza las dificultades de comprensión de la aproximación de la distribución binomial por la normal, surgida de la práctica docente. Como primera etapa se considera un estudio histórico y el análisis de libros de texto como los elementos que configuran e influyen en el problema profesional. Como consecuencia, se plantea un diseño de implementación mediante representaciones de simulación para facilitar la comprensión progresiva y su generalización al estudio del teorema central del límite.This paper describes a reflection process on the teaching of statistics at university level. It also discusses the difficulties of understanding the binomial approximation of the normal distribution, as a result of the teaching practice. As a first step, a historical study and analysis of textbooks is considered, as well as the elements that shape and influence professional issues. As a result, an implementation design is proposed through simulated representations to facilitate the progressive understanding and generalization to the study of central limit theorem.
New Classes of Permutation Binomials and Permutation Trinomials over Finite Fields
Li, Kangquan; Qu, Longjiang; Chen, Xi
2015-01-01
Permutation polynomials over finite fields play important roles in finite fields theory. They also have wide applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, communication theory and so on. Permutation binomials and trinomials attract people's interest due to their simple algebraic form and additional extraordinary properties. In this paper, several new classes of permutation binomials and permutation trinomials are constructed. ...
Wang, Xiao-Guang; Pan, Shao-Hua; Yang, Guo-Zhen
1999-01-01
We study the nonclassical properties and algebraic characteristics of the negative binomial states introduced by Barnett recently. The ladder operator formalism and displacement operator formalism of the negative binomial states are found and the algebra involved turns out to be the SU(1,1) Lie algebra via the generalized Holstein-Primarkoff realization. These states are essentially Peremolov's SU(1,1) coherent states. We reveal their connection with the geometric states and find that they ar...
On Bivariate Generalized Exponential-Power Series Class of Distributions
Jafari, Ali Akbar; Roozegar, Rasool
2015-01-01
In this paper, we introduce a new class of bivariate distributions by compounding the bivariate generalized exponential and power-series distributions. This new class contains some new sub-models such as the bivariate generalized exponential distribution, the bivariate generalized exponential-poisson, -logarithmic, -binomial and -negative binomial distributions. We derive different properties of the new class of distributions. The EM algorithm is used to determine the maximum likelihood estim...
Statistical Yield Modeling for IC Manufacture: Hierarchical Fault Distributions
Bogdanov, Yu. I.; Bogdanova, N. A.; Dshkhunyan, V. L.
2003-01-01
A hierarchical approach to the construction of compound distributions for process-induced faults in IC manufacture is proposed. Within this framework, the negative binomial distribution and the compound binomial distribution are treated as level-1 models. The hierarchical approach to fault distribution offers an integrated picture of how fault density varies from region to region within a wafer, from wafer to wafer within a batch, and so on. A theory of compound-distribution hierarchies is de...
Verification of rod safety via confidence intervals for a binomial proportion
International Nuclear Information System (INIS)
The probabilistic safety assessed to a set of N fuel rods assembled in one core of a nuclear power reactor is commonly modelled by Σ i≤N X i, where X 1, ..., X N are independent Bernoulli random variables (rv) with individual probability p i = P (X i = 1) that the ith rod shows no failure during one cycle. This is the probability of the event that the ith rod will not exceed the failure limit during one cycle. The safety standard presently set by the German Reaktor-Sicherheitskommission (Reactor Safety Commission) requires that the expected number of unfailed rods in the core during one cycle is at least N - 1, i.e., E(Σ i≤N X i) = Σ i≤N p i ≥ N - 1, whereby a confidence level of 0.95 for the verification of this condition is demanded. In this paper, we provide an approach, based on the Clopper-Pearson confidence interval for the proportion p of a binomial B(n, p) distribution, how to verify this condition with a confidence level of at least 0.95. We extend our approach to the case, where the set of N fuel rods is arranged in strata, possibly due to different design in each stratum
Effects of the Detection Efficiency on Multiplicity Distributions
Tang, A
2013-01-01
In this paper we investigate how a finite detection efficiency affects three popular multiplicity distributions, namely the Poisson, the Binomial and the Negative Binomial distributions. We found that a constant detection efficiency does not change the characteristic of a distribution, while a variable detection efficiency does. We layout a procedure to study the deviation of moments from the baseline distribution due to a variable detection efficiency.
Effects of the detection efficiency on multiplicity distributions
Tang, A. H.; Wang, G.
2013-08-01
In this paper we investigate how a finite detection efficiency affects three popular multiplicity distributions, namely, the Poisson, the binomial, and the negative binomial distributions. We found that a multiplicity-independent detection efficiency does not change the characteristic of a distribution, while a multiplicity-dependent detection efficiency does. We layout a procedure to study the deviation of moments and their derivative quantities from the baseline distribution due to a multiplicity-dependent detection efficiency.
Effects of the Detection Efficiency on Multiplicity Distributions
Tang, A; Wang, G
2013-01-01
In this paper we investigate how a finite detection efficiency affects three popular multiplicity distributions, namely the Poisson, the Binomial and the Negative Binomial distributions. We found that a multiplicity-independent detection efficiency does not change the characteristic of a distribution, while a multiplicity-dependent detection efficiency does. We layout a procedure to study the deviation of moments and their derivative quantities from the baseline distribution due to a multipli...
Disoriented Chiral Condensates, Pion Probability Distributions and Parallels with Disordered System
Mekjian, A. Z.
1999-01-01
A general expression is discussed for pion probability distributions coming from relativistic heavy ion collisions. The general expression contains as limits: 1) The disoriented chiral condensate (DCC), 2) the negative binomial distribution and Pearson type III distribution, 3) a binomial or Gaussian result, 4) and a Poisson distribution. This general expression approximates other distributions such as a signal to noise laser distribution. Similarities and differences of the DCC distribution ...
Institute of Scientific and Technical Information of China (English)
范洪义; 吴泽
2015-01-01
According to the combinational binomial-negative-binomial distribution, we propose a binomial-negative-binomial combinational optical field state, which can be generated in the process of a Fock state |m⟩⟨m| passing through a quantum-mechanical diffusion channel. We derive the second-order coherence degree formula, g(2) (t)=2− m2+m(m+κt)2 , which is the diffusion constant. We find that in the process of the Fock state undergoing quantum diffusion and becoming classical, the corresponding photon statistics evolves from sub-Poissonian distribution to Poisson distribution and finally goes to a chaotic state. We also find that the more photons in the initial Fock state, the longer time is needed for quantum decoherence.%在组合二项-负二项分布的基础上,提出了二项-负二项组合光场态,这种态能在Fo ck态历经量子扩散通道的过程中实现。导出了此光场的二阶相干度公式, g(2)(t)=2− m2+m(m+κt)2,发现随着时间的推移光场从非经典Fock态变为经典态,光子数m经扩散通道后变成了m+κt,κ是扩散常数,相应的光子统计从亚泊松分布历经泊松分布再变成混沌光；初始Fo ck态的光子数越多,则扩散所需的时间越长。
Relacionando las distribuciones binomial negativa y logarítmica vía sus series asociadas
Sadinle, Mauricio
2011-01-01
La distribución binomial negativa está asociada a la serie obtenida de derivar la serie logarítmica. Recíprocamente, la distribución logarítmica está asociada a la serie obtenida de integrar la serie asociada a la distribución binomial negativa. El parámetro del número de fallas de la distribución Binomial negativa es el número de derivadas necesarias para obtener la serie binomial negativa de la serie logarítmica. El razonamiento presentado puede emplearse como un método alternativo para pro...
Bhunya, P. K.; Berndtsson, R.; Jain, Sharad. K.; Kumar, Rakesh
2013-08-01
Two flood analysis estimation schemes, based on, respectively, partial duration series (PDS) and annual maximum series (AMS), are compared. The PDS model assumes a Generalized Pareto (GP) distribution for modeling the flood exceedances above threshold corresponding to a generalized extreme value (GEV) distribution for annual maxima. As a generalization of the common assumption of the Poisson distribution (PD) to count the occurrences of peaks over threshold in the PDS models, the advantage of negative binomial (NB) distribution is explored in this study. The T-year event estimator for the annual maximum distribution corresponding to the parent PDS model is formulated for producing AMS samples consistent with PDS samples which are used in simulations. The performance of the two models in terms of the uncertainty of the T-year event estimator is evaluated in the cases of estimation with the method of probability weighted moments (PWM). In a similar way, the performance of the derived PDS/NB-GP model is compared with the existing PDS/PD-GP model in terms of uncertainty of T-year event estimator using simulation and field data. The results show the T-year event estimate using PDS/NB-GP model yields lower variance compared to PDS/PD-GP models for most cases. However both the models perform similarly at higher return periods more than 300 years, using the ratios of the variance of T-years estimate as an index, and the ratio decreases with an increase in mean number of annual exceedances above threshold (μ). From the results it is observed that both AMS and PDS models yield the same variance when μ varies from 1.4 to 1.65. However, in case of NB distribution the PDS and AMS models gives the same variance of q(T) when variance (σ2) is 1.5 times the mean number of annual exceedance above threshold. The performance of the PDS models and the corresponding AMS models using the available data of Dee (at Cairnton) shows the PDS/NB-GP model to be marginally better at return
Institute of Scientific and Technical Information of China (English)
刘堂昆; 张康隆; 陶宇; 单传家; 刘继兵
2016-01-01
The temporal evolution of the degree of entanglement between two atoms in a system of the binomial optical field interacting with two arbitrary entangled atoms is investigated. The influence of the strength of the dipole–dipole interaction between two atoms, probabilities of the Bernoulli trial, and particle number of the binomial optical field on the temporal evolution of the atomic entanglement are discussed. The result shows that the two atoms are always in the entanglement state. Moreover, if and only if the two atoms are initially in the maximally entangled state, the entanglement evolution is not affected by the parameters, and the degree of entanglement is always kept as 1.
Entanglement and photon statistics of output fields from beam splitter for binomial state inputs
Institute of Scientific and Technical Information of China (English)
Zhou Qing-Ping; Fang Mao-Fa
2004-01-01
The entanglement properties are investigated based on linear entropy, and nonclassicalities are examined of output fields from a beam splitter for pure binomial state inputs. It is shown that the properties of the entanglement and the photon statistics of output fields are not only strongly dependent on the parameters of input binomial states but also quite involved with the nature of the beam splitter. The best entanglement can be obtained when the parameters of both input states and the beam splitter are chosen appropriately. Finally, we analyse briefly the distinguishability between the joint input state and the joint output state.
On negative binomial approximation to k-runs
Wang, Xiaoxin; Xia, Aihua
2008-01-01
The distributions of the run occurrences for a sequence of independent and identically distributed (i.i.d.) experiments are usually obtained by combinatorial methods (see Balakrishnan and Koutras (2002, Chapter 5)) and the resulting formulae are often very tedious, while the distributions for non i.i.d. experiments are generally intractable. It is therefore of practical interest to find a suitable approximate model with reasonable approximation accuracy. In this paper we ...
Suzuki, N.; Biyajima, M.; Nakajima, N
1996-01-01
Newly reported normalized cumulant moments of charged particles in $e^+e^-$ collisions by the SLD collaboration are analyzed by the truncated modified negative binomial distribution (MNBD) and the negative binomial distribution (NBD). Calculated result by the MNBD describes the oscillatory behavior of the data much better than that by the NBD.
DEFF Research Database (Denmark)
Vilsen, Søren B.; Tvedebrink, Torben; Mogensen, Helle Smidt;
2015-01-01
function and (2) we used the expectation-maximisation, EM, algorithm. The estimated parameters were used to create dynamic, sample specific thresholds for noise removal using marker specific proportions of the negative binomial distribution. Based on data from dilution series experiments (amounts of DNA...... ranging from 100 pg to 2 ng) conducted at The Section of Forensic Genetics, Department of Forensic Medicine, Faculty of Health and Medical Sciences, University of Copenhagen, Denmark, the method was compared to that of a naïve model that implies the removal of reads with a coverage of less than 5–10% of...
Overdispersion: Notes on discrete distributions
Energy Technology Data Exchange (ETDEWEB)
Bowman, K.O. [Oak Ridge National Lab., TN (United States); Shenton, L.R. [Georgia Univ., Athens, GA (United States); Kastenbaum, M.A. [Ft. Myers, Florida (United States); Broman, K. [Wisconsin Univ., Milwaukee, WI (United States)
1992-09-01
We introduce mixtures of binomial distributions derived by assuming that the probability parameter p varies according to some law. We use the transformation p = exp({minus}t) and consider various appropriate densities for the transformed variables. In the process, the Laplace transform becomes the fundamental entity. Large numbers of new binomial mixtures are generated in this way. Some transformations may involve several variates that lead to ``multivariate`` binomial mixtures. An extension of this to the logarithmic distribution, with parameter p, is possible. Frullani integrals and Laplace transforms are encountered. Graphical representations of some of the more significant distributions are given. These include probability functions, regions of validity, and three dimensional representations of probability functions showing the response to variation of parameters when two parameters are involved.
Overdispersion: Notes on discrete distributions
Energy Technology Data Exchange (ETDEWEB)
Bowman, K.O. (Oak Ridge National Lab., TN (United States)); Shenton, L.R. (Georgia Univ., Athens, GA (United States)); Kastenbaum, M.A. (Ft. Myers, Florida (United States)); Broman, K. (Wisconsin Univ., Milwaukee, WI (United States))
1992-09-01
We introduce mixtures of binomial distributions derived by assuming that the probability parameter p varies according to some law. We use the transformation p = exp([minus]t) and consider various appropriate densities for the transformed variables. In the process, the Laplace transform becomes the fundamental entity. Large numbers of new binomial mixtures are generated in this way. Some transformations may involve several variates that lead to multivariate'' binomial mixtures. An extension of this to the logarithmic distribution, with parameter p, is possible. Frullani integrals and Laplace transforms are encountered. Graphical representations of some of the more significant distributions are given. These include probability functions, regions of validity, and three dimensional representations of probability functions showing the response to variation of parameters when two parameters are involved.
Extended Conway-Maxwell-Poisson distribution and its properties and applications
Chakraborty, Subrata; Imoto, Tomoaki
2015-01-01
A new three parameter natural extension of the Conway-Maxwell-Poisson (COM-Poisson) distribution is proposed. This distribution includes the recently proposed COM-Poisson type negative binomial (COM-NB) distribution [Chakraborty, S. and Ong, S. H. (2014): A COM-type Generalization of the Negative Binomial Distribution, Accepted in Communications in Statistics-Theory and Methods] and the generalized COM-Poisson (GCOMP) distribution [Imoto, T. :(2014) A generalized Conway-Maxwell-Poisson distri...
Joint Analysis of Binomial and Continuous Traits with a Recursive Model
DEFF Research Database (Denmark)
Varona, Louis; Sorensen, Daniel
2014-01-01
This work presents a model for the joint analysis of a binomial and a Gaussian trait using a recursive parametrization that leads to a computationally efficient implementation. The model is illustrated in an analysis of mortality and litter size in two breeds of Danish pigs, Landrace and Yorkshire...
The Euler Series Transformation and the Binomial Identities of Ljunggren, Munarini and Simons
Boyadzhiev, Khristo N.
2009-01-01
It is shown that the curious identity of Simons follows immediately from Euler's series transformation formula and also from an identity due to Ljunggren. The relation of Simons' identity to Legendre's polynomials is also discussed. At the end we use the generalized Euler series transformation to obtain two recent binomial identities of Munarini.
On the Residues of Binomial Coefficients and Their Products Modulo Prime Powers
Institute of Scientific and Technical Information of China (English)
CAI Tian Xin; GRANVILLE Andrew
2002-01-01
In this paper, we show several arithmetic properties on the residues of binomial coefficients and their products modulo prime powers, e.g.,((pq-1 (pq-1)/2)≡ (p-1 (p-1)/2)(q-1 (q-1)/2)(modpq),for any distinct odd primes p and q. Meanwhile, we discuss the connections with the prime recognitions.
Franco, R. Lo; Compagno, G; Messina, A.; Napoli, A.
2007-01-01
We introduce the $N$-photon quantum superposition of two orthogonal generalized binomial states of electromagnetic field. We then propose, using resonant atom-cavity interactions, non-conditional schemes to generate and reveal such a quantum superposition for the two-photon case in a single-mode high-$Q$ cavity. We finally discuss the implementation of the proposed schemes.
Exact Kolmogorov and total variation distances between some familiar discrete distributions
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We give exact closed-form expressions for the Kolmogorov and the total variation distances between Poisson, binomial, and negative binomial distributions with different parameters. In the Poisson case, such expressions are related with the Lambert W function.
Deconvoluting preferences and errors: a model for binomial panel data
DEFF Research Database (Denmark)
Fosgerau, Mogens; Nielsen, Søren Feodor
2010-01-01
In many stated choice experiments researchers observe the random variables Vt, Xt, and Yt = 1{U + δxs22A4Xt + εt
A Negative Binomial Regression Model for Accuracy Tests
Hung, Lai-Fa
2012-01-01
Rasch used a Poisson model to analyze errors and speed in reading tests. An important property of the Poisson distribution is that the mean and variance are equal. However, in social science research, it is very common for the variance to be greater than the mean (i.e., the data are overdispersed). This study embeds the Rasch model within an…
Frequency distribution of coliforms in water distribution systems.
Christian, R R; Pipes, W O
1983-01-01
Nine small water distribution systems were sampled intensively to determine the patterns of dispersion of coliforms. The frequency distributions of confirmed coliform counts were compatible with either the negative-binomial or the lognormal distribution. They were not compatible with either the Poisson or Poisson-plus-added zeroes distribution. The implications of the use of the lognormal distributional model were further evaluated because of its previous use in water quality studies. The geo...
Louis Laurencelle
2012-01-01
Pascal distribution, Pa(r, /pi), also called Negative binomial distribution, pertains to the trial number n at which the first r successes have been obtained, each trial being the realization of a Bernoulli variable with success probability /pi. We review basic concepts of the Bernoulli process and delve into the constrained Pascal distribution, or Negative binomial distribution of order k, Pa(r, k, /pi), which concerns the trial number n at which r successes have been recorded within the las...
Directory of Open Access Journals (Sweden)
James A Wiley
Full Text Available We put forward a new item response model which is an extension of the binomial error model first introduced by Keats and Lord. Like the binomial error model, the basic latent variable can be interpreted as a probability of responding in a certain way to an arbitrarily specified item. For a set of dichotomous items, this model gives predictions that are similar to other single parameter IRT models (such as the Rasch model but has certain advantages in more complex cases. The first is that in specifying a flexible two-parameter Beta distribution for the latent variable, it is easy to formulate models for randomized experiments in which there is no reason to believe that either the latent variable or its distribution vary over randomly composed experimental groups. Second, the elementary response function is such that extensions to more complex cases (e.g., polychotomous responses, unfolding scales are straightforward. Third, the probability metric of the latent trait allows tractable extensions to cover a wide variety of stochastic response processes.
Directory of Open Access Journals (Sweden)
Qingyu An
Full Text Available The hand foot and mouth disease (HFMD is a human syndrome caused by intestinal viruses like that coxsackie A virus 16, enterovirus 71 and easily developed into outbreak in kindergarten and school. Scientifically and accurately early detection of the start time of HFMD epidemic is a key principle in planning of control measures and minimizing the impact of HFMD. The objective of this study was to establish a reliable early detection model for start timing of hand foot mouth disease epidemic in Dalian and to evaluate the performance of model by analyzing the sensitivity in detectability.The negative binomial regression model was used to estimate the weekly baseline case number of HFMD and identified the optimal alerting threshold between tested difference threshold values during the epidemic and non-epidemic year. Circular distribution method was used to calculate the gold standard of start timing of HFMD epidemic.From 2009 to 2014, a total of 62022 HFMD cases were reported (36879 males and 25143 females in Dalian, Liaoning Province, China, including 15 fatal cases. The median age of the patients was 3 years. The incidence rate of epidemic year ranged from 137.54 per 100,000 population to 231.44 per 100,000population, the incidence rate of non-epidemic year was lower than 112 per 100,000 population. The negative binomial regression model with AIC value 147.28 was finally selected to construct the baseline level. The threshold value was 100 for the epidemic year and 50 for the non- epidemic year had the highest sensitivity(100% both in retrospective and prospective early warning and the detection time-consuming was 2 weeks before the actual starting of HFMD epidemic.The negative binomial regression model could early warning the start of a HFMD epidemic with good sensitivity and appropriate detection time in Dalian.
Application of a binomial cusum control chart to monitor one drinking water indicator
Directory of Open Access Journals (Sweden)
Elisa Henning
2014-02-01
Full Text Available The aim of this study is to analyze the use of a binomial cumulative sum chart (CUSUM to monitor the presence of total coliforms, biological indicators of quality of water supplies in water treatment processes. The sample series were monthly taken from a water treatment plant and were analyzed from 2007 to 2009. The statistical treatment of the data was performed using GNU R, and routines were created for the approximation of the upper limit of the binomial CUSUM chart. Furthermore, a comparative study was conducted to investigate whether there is a significant difference in sensitivity between the use of CUSUM and the traditional Shewhart chart, the most commonly used chart in process monitoring. The results obtained demonstrate that this study was essential for making the right choice in selecting a chart for the statistical analysis of this process.
Modeling and Predistortion of Envelope Tracking Power Amplifiers using a Memory Binomial Model
DEFF Research Database (Denmark)
Tafuri, Felice Francesco; Sira, Daniel; Larsen, Torben
2013-01-01
Nowadays envelope tracking (ET) is considered one of the most appealing techniques for the efficiency enhancement of RF power amplifiers (PAs), but it also introduces a number of additional challenges for the system simulation and implementation. In this context, this paper aims to provide a new...... behavioral model capable of an improved performance when used for the modeling and predistortion of RF PAs deployed in ET transceivers. The proposed solution consists in a 2D behavioral model having as a dual-input the PA complex baseband envelope and the modulated supply waveform, peculiar of the ET case....... The model definition is based on binomial series, hence the name of memory binomial model (MBM). The MBM is here applied to measured data-sets acquired from an ET measurement set-up. When used as a PA model the MBM showed an NMSE (Normalized Mean Squared Error) as low as −40dB and an ACEPR (Adjacent...
International Nuclear Information System (INIS)
Purpose: To introduce multilevel binomial logistic prediction model-based computer-aided diagnostic (CAD) method of small solitary pulmonary nodules (SPNs) diagnosis by combining patient and image characteristics by textural features of CT image. Materials and methods: Describe fourteen gray level co-occurrence matrix textural features obtained from 2171 benign and malignant small solitary pulmonary nodules, which belongs to 185 patients. Multilevel binomial logistic model is applied to gain these initial insights. Results: Five texture features, including Inertia, Entropy, Correlation, Difference-mean, Sum-Entropy, and age of patients own aggregating character on patient-level, which are statistically different (P < 0.05) between benign and malignant small solitary pulmonary nodules. Conclusion: Some gray level co-occurrence matrix textural features are efficiently descriptive features of CT image of small solitary pulmonary nodules, which can profit diagnosis of earlier period lung cancer if combined patient-level characteristics to some extent.
Estimación del riesgo relativo mediante el modelo log-binomial
Pérez Fernández, Silvia
2016-01-01
A pesar de que el modelo de regresión log-binomial permite la estimación del riesgo relativo (RR) es un modelo poco usado en la epidemiología. Se suele usar con mucha más frecuencia el modelo de regresión logística que provee una estimación del odds ratio (OR) y, de esta manera, una aproximación del RR. No obstante, la estimación del RR mediante el OR puede ser errónea. En este trabajo se presenta con detalle el modelo log-binomial poniendo énfasis en los problemas computacionales que pueden ...
Estimation of a probability with optimum guaranteed confidence in inverse binomial sampling
Mendo Tomás, Luis; Hernando Rábanos, José María
2010-01-01
Sequential estimation of a probability p by means of inverse binomial sampling is considered. For μ1, μ2>1 given, the accuracy of an estimator ̂p is measured by the confidence level P[p/μ2≤̂p≤pμ1]. The confidence levels c0 that can be guaranteed for p unknown, that is, such that P[p/μ2≤̂p≤pμ1]≥c0 for all p∈(0, 1), are investigated. It is shown that within the general class of randomized or non-randomized estimators based on inverse binomial sampling, there is a maximum c0 that can be guarante...
Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams
International Nuclear Information System (INIS)
Nested sums containing binomial coefficients occur in the computation of massive operatormatrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss algorithms for converting between sum and integral representations, mainly relying on the Mellin transform. To aid the conversion we worked out dedicated rewrite rules, based on which also some general patterns emerging in the process can be obtained.
Generalized harmonic, cyclotomic, and binomial sums, their polylogarithms and special numbers
International Nuclear Information System (INIS)
A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of special numbers. Starting with harmonic sums and polylogarithms we discuss recent extensions of these quantities as cyclotomic, generalized (cyclotomic), and binomially weighted sums, associated iterated integrals and special constants and their relations.
Testing for Serial Dependence in Binomial Time Series I: Parameter Driven Models
Dunsmuir, W. T. M.; He, J. Y.
2016-01-01
Binomial time series in which the logit of the probability of success is modelled as a linear function of observed regressors and a stationary latent Gaussian process are considered. Score tests are developed to first test for the existence of a latent process and, subsequent to that, evidence of serial dependence in that latent process. The test for the existence of a latent process is important because, if one is present, standard logistic regression methods will produce inconsistent estima...
Liu-type Negative Binomial Regression: A Comparison of Recent Estimators and Applications
Asar, Yasin
2016-01-01
This paper introduces a new biased estimator for the negative binomial regression model that is a generalization of Liu-type estimator proposed for the linear model in [12]. Since the variance of the maximum likelihood estimator (MLE) is inflated when there is multicollinearity between the explanatory variables, a new biased estimator is proposed to solve the problem and decrease the variance of MLE in order to make stable inferences. Moreover, we obtain some theoretical comparisons between t...
Generalized harmonic, cyclotomic, and binomial sums, their polylogarithms and special numbers
Energy Technology Data Exchange (ETDEWEB)
Ablinger, J.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, J. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2013-10-15
A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of special numbers. Starting with harmonic sums and polylogarithms we discuss recent extensions of these quantities as cyclotomic, generalized (cyclotomic), and binomially weighted sums, associated iterated integrals and special constants and their relations.
Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams
Ablinger, Jakob; Raab, Clemens G; Schneider, Carsten
2014-01-01
Nested sums containing binomial coefficients occur in the computation of massive operator matrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss algorithms for converting between sum and integral representations, mainly relying on the Mellin transform. To aid the conversion we worked out dedicated rewrite rules, based on which also some general patterns emerging in the process can be obtained.
Wan, Zhi-Long; Fan, Hong-Yi
2016-02-01
For the density operator (mixed state) describing chaotic light and negative-binomial field there exist the corresponding thermal vacuum state (pure state) in the real-fictitious space. Using the method of integration within ordered product of operators we find the expectation value theorem in these two thermo vacuum states respectively. The thermal average theorem of translation operator is also deduced. Application of the new thermo vacuum state in calculating photon number disturibution and fluctuation and thermal average is presented.
Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams
Energy Technology Data Exchange (ETDEWEB)
Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, Johannes; Raab, Clemens G. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)
2014-07-15
Nested sums containing binomial coefficients occur in the computation of massive operatormatrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss algorithms for converting between sum and integral representations, mainly relying on the Mellin transform. To aid the conversion we worked out dedicated rewrite rules, based on which also some general patterns emerging in the process can be obtained.
2014-01-01
A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics, and theoretical physics. Here we show how one can obtain further interesting and (almost) serendipitous identities about certain finite or infinite series involving binomial coefficients, harmonic numbers...
A spatial Beta-Binomial model for clustered count data on dental caries
Bandyopadhyay, Dipankar; Reich, Brian J.; Slate, Elizabeth H
2010-01-01
One of the most important indicators of dental caries prevalence is the total count of decayed, missing or filled (DMF) surfaces in a tooth. These count data are often clustered in nature (several count responses clustered within a subject), over-dispersed, as well as spatially referenced (a diseased tooth might be positively influencing the decay process of a set of neighboring teeth). In this paper, we develop a multivariate spatial Beta-Binomial (BB) model for these data that accommodates ...
E. Andres Houseman; Brent Coull; James Shine
2004-01-01
Boston Harbor has had a history of poor water quality, including by enteric pathogens. We conduct a statistical analysis of data collected by the Massachusetts Water Resources Authority (MWRA) between 1996 and 2002 to evaluate the effects of court-mandated improvements in sewage treatment. We propose a negative binomial model for time series of Enterococcus counts in Boston Harbor, where nonstationarity and autocorrelation are modeled using a nonparametric smooth function of time in the predi...
Multiple analogues of binomial coefficients and related families of special numbers
Coskun, Hasan
2010-01-01
We construct multiple $qt$-binomial coefficients and related multiple analogues of several celebrated families of special numbers in this paper. These multidimensional generalizations include the first and the second kind of $qt$-Stirling numbers, $qt$-Bell numbers, $qt$-Bernoulli numbers, $qt$-Catalan numbers and the $qt$--Fibonacci numbers. In the course of developing main properties of these extensions, we prove results that are significant in their own rights such as certain probability m...
Bethe states for the two-site Bose-Hubbard model: a binomial approach
Santos, Gilberto; Foerster, Angela; Roditi, Itzhak
2015-01-01
We calculate explicitly the Bethe vectors states by the algebraic Bethe ansatz method with the $gl(2)$-invariant $R$-matrix for the two-site Bose-Hubbard model. Using a binomial expansion of the n-th power of a sum of two operators we get and solve a recursion equation. We calculate the scalar product and the norm of the Bethe vectors states. The form factors of the imbalance current operator are also computed.
Sorana BOLBOACĂ
2005-01-01
In trial, when the results are reported as dichotomies variables, the most important measure of effect are represented by the relative risk reduction, absolute risk reduction and number needed to treat, providing the basis for clinicians to balance the benefits and harms of therapy for their patients. The relative risk reduction is a very useful parameter in assessment of a treatment effect if it is accompanied by confidence intervals. The only method used in medical article for computing the...
Directory of Open Access Journals (Sweden)
Sorana BOLBOACĂ
2005-01-01
Full Text Available In trial, when the results are reported as dichotomies variables, the most important measure of effect are represented by the relative risk reduction, absolute risk reduction and number needed to treat, providing the basis for clinicians to balance the benefits and harms of therapy for their patients. The relative risk reduction is a very useful parameter in assessment of a treatment effect if it is accompanied by confidence intervals. The only method used in medical article for computing the confidence intervals for relative risk reduction is the asymptotic method. The aim the research was to propose some new methods of computing confidence intervals for relative risk reduction and relative risk reduction like parameters and to compare these methods with the asymptotic one in order to assess their performance.In order to estimate the confidence intervals for relative risk reduction we proposed based on the literature definitions and on our experiences in confidence intervals five methods called here ARPWald, ARPAC, ARPWaldC1, ARPWaldC2, and ARPWaldC3. The criterions of assessment were represented by the upper and lower boundaries, the average of experimental errors and standard deviations, and the deviation relative to imposed significance level α equal with 5%. All methods were assessed on random variables (X, Y and random samples sizes (n, m.Chousing a method of computing confidence intervals for relative risk reduction (RRR and RRR-like functions depend on objective of research. If we desire a method which to obtain performance in estimating the average of the experimental errors we can chouse the ARPWald method, while if we need a method with the smallest deviation we will chouse the ARPAC method.
Estimasi Harga Multi-State European Call Option Menggunakan Model Binomial
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Mila Kurniawaty, Endah Rokhmati
2011-05-01
Full Text Available Option merupakan kontrak yang memberikan hak kepada pemiliknya untuk membeli (call option atau menjual (put option sejumlah aset dasar tertentu (underlying asset dengan harga tertentu (strike price dalam jangka waktu tertentu (sebelum atau saat expiration date. Perkembangan option belakangan ini memunculkan banyak model pricing untuk mengestimasi harga option, salah satu model yang digunakan adalah formula Black-Scholes. Multi-state option merupakan sebuah option yang payoff-nya didasarkan pada dua atau lebih aset dasar. Ada beberapa metode yang dapat digunakan dalam mengestimasi harga call option, salah satunya masyarakat finance sering menggunakan model binomial untuk estimasi berbagai model option yang lebih luas seperti multi-state call option. Selanjutnya, dari hasil estimasi call option dengan model binomial didapatkan formula terbaik berdasarkan penghitungan eror dengan mean square error. Dari penghitungan eror didapatkan eror rata-rata dari masing-masing formula pada model binomial. Hasil eror rata-rata menunjukkan bahwa estimasi menggunakan formula 5 titik lebih baik dari pada estimasi menggunakan formula 4 titik.
Quadrupolar-coupling-specific binomial pulse sequences for in vivo 23Na NMR and MRI.
Laustsen, Christoffer; Ringgaard, Steffen; Pedersen, Michael; Nielsen, Niels Chr
2010-09-01
Aimed at selective detection of (23)Na with specific quadrupolar couplings for in vitro NMR and MRI, we present a series of quadrupolar binomial pulse sequences offering high specificity with respect to the quadrupolar couplings of the excited species. It is demonstrated that pulse sequences with an increasing number of elements, e.g., 11, 121, 1331, 14641, and 15101051, with the units representing flip angles smaller than the 90 degrees pulses typically encountered in binomial spin-1/2 solvent suppression experiments, and different phase combinations may provide a high degree of flexibility with respect to quadrupolar coupling selectivity and robustness towards rf inhomogeneity. This may facilitate efficient separation of, for example, intra and extracellular (23)Na in tissues with efficient control of the excitation (or suppression) of central as well as satellite transitions through on- and off-resonance irradiation. The pulse sequences are described in terms of their analogy to binomial liquid-state NMR solvent suppression experiments and demonstrated numerically and experimentally through NMR and MRI experiments on a 7 T horizontal small-bore animal magnet system. PMID:20673642
Analysis of railroad tank car releases using a generalized binomial model.
Liu, Xiang; Hong, Yili
2015-11-01
The United States is experiencing an unprecedented boom in shale oil production, leading to a dramatic growth in petroleum crude oil traffic by rail. In 2014, U.S. railroads carried over 500,000 tank carloads of petroleum crude oil, up from 9500 in 2008 (a 5300% increase). In light of continual growth in crude oil by rail, there is an urgent national need to manage this emerging risk. This need has been underscored in the wake of several recent crude oil release incidents. In contrast to highway transport, which usually involves a tank trailer, a crude oil train can carry a large number of tank cars, having the potential for a large, multiple-tank-car release incident. Previous studies exclusively assumed that railroad tank car releases in the same train accident are mutually independent, thereby estimating the number of tank cars releasing given the total number of tank cars derailed based on a binomial model. This paper specifically accounts for dependent tank car releases within a train accident. We estimate the number of tank cars releasing given the number of tank cars derailed based on a generalized binomial model. The generalized binomial model provides a significantly better description for the empirical tank car accident data through our numerical case study. This research aims to provide a new methodology and new insights regarding the further development of risk management strategies for improving railroad crude oil transportation safety. PMID:26298272
Multiplicity Distributions in QCD at Very High Energies
Dremin, I. M.
1994-01-01
Recent results in QCD on multiplicity distributions are briefly reviewed. QCD is able to predict very tiny features of multiplicity distributions which demonstrate that the negative binomial distribution (and, more generally, any infinitely divisible distribution) is inappropriate for precise description of experimental data. New fits of high energy multiplicity distributions can be derived.
Nakajima, N; Biyajima, M.; Suzuki, N.
1996-01-01
Oscillatory behavior of cumulant moments obtained from the experimental data in $pp$ collisions and $\\bar{p}p$ collisions are analyzed by the modified negative binomial distribution (MNBD) and the negative binomial distribution (NBD). Both distributions well describe the cumulant moments obtained from the data. This fact shows sharp contrast to the result in $e^+e^-$ collisions, which is described by the the MNBD much better than by the NBD.
Nonextensive Statistics and Multiplicity Distribution in Hadronic Collisions
Aguiar, C. E.; Kodama, T.
2002-01-01
The multiplicity distribution of particles in relativistic gases is studied in terms of Tsallis' nonextensive statistics. For an entropic index q>1 the multiplicity distribution is wider than the Poisson distribution with the same average number of particles, being similar to the negative binomial distribution commonly used in phenomenological analysis of hadron production in high-energy collisions.
Stochastic Models for the Distribution of Index Terms.
Nelson, Michael J.
1989-01-01
Presents a probability model of the occurrence of index terms used to derive discrete distributions which are mixtures of Poisson and negative binomial distributions. These distributions give better fits than the simpler Zipf distribution, have the advantage of being more explanatory, and can incorporate a time parameter if necessary. (25…
Constructing Binomial Trees Via Random Maps for Analysis of Financial Assets
Directory of Open Access Journals (Sweden)
Antonio Airton Carneiro de Freitas
2010-04-01
Full Text Available Random maps can be constructed from a priori knowledge of the financial assets. It is also addressed the reverse problem, i.e. from a function of an empirical stationary probability density function we set up a random map that naturally leads to an implied binomial tree, allowing the adjustment of models, including the ability to incorporate jumps. An applica- tion related to the options market is presented. It is emphasized that the quality of the model to incorporate a priori knowledge of the financial asset may be affected, for example, by the skewed vision of the analyst.
The Chernoff Modification of the Fisher Exact Test for the Difference of Two Binomial Probabilities
Takahashi, Hajime; Uematsu, Kazuki
2006-01-01
To test the difference of two binomial probabilities, we will apply the Fisher exact test modified by Chernoff (2002), which will be called CMF test. The key idea is to use the P-value of Fisher exact test as a test statistic and this makes it possible to apply the Fisher exact test for more general problems. The numerical comparison with the likelihood ratio test and the Bayes test are also conducted and we find that the performance of CMF test is close to that of the likelihood ratio test a...
“Micro” Phraseology in Action: A Look at Fixed Binomials
Directory of Open Access Journals (Sweden)
Dušan Gabrovšek
2011-06-01
Full Text Available Multiword items in English are a motley crew, as they are not only numerous but also structurally, semantically, and functionally diverse. The paper offers a fresh look at fixed binomials, an intriguing and unexpectedly heterogeneous phraseological type prototypically consisting of two lexical components with the coordinating conjunction and – less commonly but, or, (neither/ (nor – acting as the connecting element, as e.g. in body and soul, slowly but surely, sooner or later, neither fish nor fowl. In particular, their idiomaticity and lexicographical significance are highlighted, while the cross-linguistic perspective is only outlined.
Lara, Jesus R; Hoddle, Mark S
2015-08-01
Oligonychus perseae Tuttle, Baker, & Abatiello is a foliar pest of 'Hass' avocados [Persea americana Miller (Lauraceae)]. The recommended action threshold is 50-100 motile mites per leaf, but this count range and other ecological factors associated with O. perseae infestations limit the application of enumerative sampling plans in the field. Consequently, a comprehensive modeling approach was implemented to compare the practical application of various binomial sampling models for decision-making of O. perseae in California. An initial set of sequential binomial sampling models were developed using three mean-proportion modeling techniques (i.e., Taylor's power law, maximum likelihood, and an empirical model) in combination with two-leaf infestation tally thresholds of either one or two mites. Model performance was evaluated using a robust mite count database consisting of >20,000 Hass avocado leaves infested with varying densities of O. perseae and collected from multiple locations. Operating characteristic and average sample number results for sequential binomial models were used as the basis to develop and validate a standardized fixed-size binomial sampling model with guidelines on sample tree and leaf selection within blocks of avocado trees. This final validated model requires a leaf sampling cost of 30 leaves and takes into account the spatial dynamics of O. perseae to make reliable mite density classifications for a 50-mite action threshold. Recommendations for implementing this fixed-size binomial sampling plan to assess densities of O. perseae in commercial California avocado orchards are discussed. PMID:26470355
Lesion distribution, multiple infection, and the logistic increase of plant disease
Waggoner, Paul E.; Rich, Saul
1981-01-01
The lesions of few of the 112 observed cases of plant disease were randomly distributed; most were fitted by the negative binomial function with exponent ≈ 1. The proportion of healthy hosts generally equaled the frequency of zero in the negative binomial. The same course of an epidemic is calculated for the logistic increase of infected plants or for plants infected by propagules produced in proportion to lesions and distributed with exponent equal 1.
Bayesian analysis of overdispersed chromosome aberration data with the negative binomial model
International Nuclear Information System (INIS)
The usual assumption of a Poisson model for the number of chromosome aberrations in controlled calibration experiments implies variance equal to the mean. However, it is known that chromosome aberration data from experiments involving high linear energy transfer radiations can be overdispersed, i.e. the variance is greater than the mean. Present methods for dealing with overdispersed chromosome data rely on frequentist statistical techniques. In this paper, the problem of overdispersion is considered from a Bayesian standpoint. The Bayes Factor is used to compare Poisson and negative binomial models for two previously published calibration data sets describing the induction of dicentric chromosome aberrations by high doses of neutrons. Posterior densities for the model parameters, which characterise dose response and overdispersion are calculated and graphed. Calibrative densities are derived for unknown neutron doses from hypothetical radiation accident data to determine the impact of different model assumptions on dose estimates. The main conclusion is that an initial assumption of a negative binomial model is the conservative approach to chromosome dosimetry for high LET radiations. (author)
CUANDO FALLA EL SUPUESTO DE HOMOCEDASTICIDAD EN VARIABLES CON DISTRIBUCIÓN BINOMIAL
Directory of Open Access Journals (Sweden)
Edison Ramiro Vásquez
2011-01-01
Full Text Available Se utilizó el proceso de Simulación de Monte Carlopara generar poblaciones de variables aleatorias con distribuciónBinomial con varianzas homogéneas y heterogéneas; para cinco,10 y 30 observaciones por unidad experimental (n y probabi-lidad de éxito del evento de 0,10, 0,20, ¿,0,90(p. Se conformaronexperimentos en Diseño Bloques al Azar con tres, cinco y nuevetratamientos (t; cuatro y ocho réplicas(r; para cada combinaciónt-r-n, se generaron 100 experimentos. A modo de disponer deun referente de discusión, se incluyó la variante de otros 100experimentos de variables con distribución Normal, con similaresmedias y varianzas de los experimentos de datos con distribuciónBinomial. Se comprobó que el comportamiento de losindicadores: porcentaje de experimentos en que se produce unrechazo de la hipótesis H0; la potencia en el ANOVA; diferenciamínima detectada en el experimento, así como el número dediferencias entre medias de tratamientos, es similar dentro decada alternativa de análisis a través de las tres variantes;evidenciando una marcada influencia el número de observaciones por unidad experimental y el número de réplicas en estosindicadores.
Multifractal Multiplicity Distribution in Bunching-Parameter Analysis
Chekanov, S V.; Kuvshinov, V. I.
1996-01-01
A new multiplicity distribution with multifractal properties which can be used in high-energy physics and quantum optics is proposed. It may be considered as a generalization of the negative-binomial distribution. We find the structure of the generating function for such distribution and discuss its properties.
Library Circulation Distributions: Some Observations on the PLR Sample.
Brownsey, K. W. R.; Burrell, Q. L.
1986-01-01
Frequency-of-circulation distributions from 16 United Kingdom libraries participating in initial period of operation of the Public Lending Right are discussed. Differences between the libraries are highlighted, and, for each, the adequacy of various refinements of the simplest model (geometric distribution, negative binomial distribution, or mixed…
Study of multiplicity distribution in full phase space in ultra relativistic nuclear collision.
Ghosh, Dipak; Chattopadhyay, Rini; Ghosh, Anit Kumar; Dayum Jafry, Abdul; Lahiri, Madhumita; Das, Susobhan; Purkait, Krishnadas; Biswas, Biswanath; Roychoudhury, Jayanta; Deb, Argha
A comparative study has been made among three distributions - the negative binomial distribution (NBD), the generalised multiplicity distribution (GMD) and the distribution followed by the two mechanism model (TMM), in order to describe the multiplicity distribution of charged secondary particles produced in 200 A GeV 32S - AgBr interaction.
Correlation functions of XX0 Heisenberg chain, q-binomial determinants, and random walks
Energy Technology Data Exchange (ETDEWEB)
Bogoliubov, N.M.; Malyshev, C.
2014-02-15
The XX0 Heisenberg model on a cyclic chain is considered. The representation of the Bethe wave functions via the Schur functions allows to apply the well-developed theory of the symmetric functions to the calculation of the thermal correlation functions. The determinantal expressions of the form-factors and of the thermal correlation functions are obtained. The q-binomial determinants enable the connection of the form-factors with the generating functions both of boxed plane partitions and of self-avoiding lattice paths. The asymptotical behavior of the thermal correlation functions is studied in the limit of low temperature provided that the characteristic parameters of the system are large enough.
Correlation Functions of XX0 Heisenberg Chain, q-Binomial Determinants, and Random Walks
Bogoliubov, N M
2014-01-01
The XX0 Heisenberg model on a cyclic chain is considered. The representation of the Bethe wave functions via the Schur functions allows to apply the well-developed theory of the symmetric functions to the calculation of the thermal correlation functions. The determinantal expressions of the form-factors and of the thermal correlation functions are obtained. The q-binomial determinants enable the connection of the form-factors with the generating functions both of boxed plane partitions and of self-avoiding lattice paths. The asymptotical behavior of the thermal correlation functions is studied in the limit of low temperature provided that the characteristic parameters of the system are large enough.
Correlation functions of XX0 Heisenberg chain, q-binomial determinants, and random walks
Bogoliubov, N. M.; Malyshev, C.
2014-02-01
The XX0 Heisenberg model on a cyclic chain is considered. The representation of the Bethe wave functions via the Schur functions allows to apply the well-developed theory of the symmetric functions to the calculation of the thermal correlation functions. The determinantal expressions of the form-factors and of the thermal correlation functions are obtained. The q-binomial determinants enable the connection of the form-factors with the generating functions both of boxed plane partitions and of self-avoiding lattice paths. The asymptotical behavior of the thermal correlation functions is studied in the limit of low temperature provided that the characteristic parameters of the system are large enough.
de Souza, R S; Killedar, M; Hilbe, J; Vilalta, R; Maio, U; Biffi, V; Ciardi, B; Riggs, J D
2014-01-01
Revealing hidden patterns in astronomical data is often the path to fundamental scientific breakthroughs; meanwhile the complexity of scientific inquiry increases as more subtle relationships are sought. Contemporary data analysis problems often elude the capabilities of classical statistical techniques, suggesting the use of cutting edge statistical methods. In this light, astronomers have overlooked a whole family of statistical techniques for exploratory data analysis and robust regression, the so-called Generalized Linear Models (GLMs). In this paper -- the first in a series aimed at illustrating the power of these methods in astronomical applications -- we elucidate the potential of a particular class of GLMs for handling binary/binomial data, the so-called logit and probit regression techniques, from both a maximum likelihood and a Bayesian perspective. As a case in point, we present the use of these GLMs to explore the conditions of star formation activity and metal enrichment in primordial minihaloes ...
Korolev, V. Yu.; Dorofeeva, A. V.
2015-01-01
Bounds of the accuracy of the normal approximation to the distribution of a sum of independent random variables are improved under relaxed moment conditions, in particular, under the absence of moments of orders higher than the second. These results are extended to Poisson-binomial, binomial and Poisson random sums. Under the same conditions, bounds are obtained for the accuracy of the approximation of the distributions of mixed Poisson random sums by the corresponding limit law. In particula...
Majumdar, Arunabha; Witte, John S; Ghosh, Saurabh
2015-12-01
Binary phenotypes commonly arise due to multiple underlying quantitative precursors and genetic variants may impact multiple traits in a pleiotropic manner. Hence, simultaneously analyzing such correlated traits may be more powerful than analyzing individual traits. Various genotype-level methods, e.g., MultiPhen (O'Reilly et al. []), have been developed to identify genetic factors underlying a multivariate phenotype. For univariate phenotypes, the usefulness and applicability of allele-level tests have been investigated. The test of allele frequency difference among cases and controls is commonly used for mapping case-control association. However, allelic methods for multivariate association mapping have not been studied much. In this article, we explore two allelic tests of multivariate association: one using a Binomial regression model based on inverted regression of genotype on phenotype (Binomial regression-based Association of Multivariate Phenotypes [BAMP]), and the other employing the Mahalanobis distance between two sample means of the multivariate phenotype vector for two alleles at a single-nucleotide polymorphism (Distance-based Association of Multivariate Phenotypes [DAMP]). These methods can incorporate both discrete and continuous phenotypes. Some theoretical properties for BAMP are studied. Using simulations, the power of the methods for detecting multivariate association is compared with the genotype-level test MultiPhen's. The allelic tests yield marginally higher power than MultiPhen for multivariate phenotypes. For one/two binary traits under recessive mode of inheritance, allelic tests are found to be substantially more powerful. All three tests are applied to two different real data and the results offer some support for the simulation study. We propose a hybrid approach for testing multivariate association that implements MultiPhen when Hardy-Weinberg Equilibrium (HWE) is violated and BAMP otherwise, because the allelic approaches assume HWE
Polynomial birth-death distribution approximation in Wasserstein distance
Xia, Aihua; Zhang, Fuxi
2008-01-01
The polynomial birth-death distribution (abbr. as PBD) on $\\ci=\\{0,1,2, >...\\}$ or $\\ci=\\{0,1,2, ..., m\\}$ for some finite $m$ introduced in Brown & Xia (2001) is the equilibrium distribution of the birth-death process with birth rates $\\{\\alpha_i\\}$ and death rates $\\{\\beta_i\\}$, where $\\a_i\\ge0$ and $\\b_i\\ge0$ are polynomial functions of $i\\in\\ci$. The family includes Poisson, negative binomial, binomial and hypergeometric distributions. In this paper, we give probabilistic proofs of variou...
Directory of Open Access Journals (Sweden)
Jianwei Zhou
2014-01-01
Full Text Available The explicit formulae of spectral norms for circulant-type matrices are investigated; the matrices are circulant matrix, skew-circulant matrix, and g-circulant matrix, respectively. The entries are products of binomial coefficients with harmonic numbers. Explicit identities for these spectral norms are obtained. Employing these approaches, some numerical tests are listed to verify the results.
Generalized distributions of order k associated with success runs in Bernoulli trials
Directory of Open Access Journals (Sweden)
Andreas N. Philippou
2003-02-01
Full Text Available In a sequence of independent Bernoulli trials, by counting multidimensional lattice paths in order to compute the probability of a first-passage event, we derive and study a generalized negative binomial distribution of order k, type I, which extends to distributions of order k, the generalized negative binomial distribution of Jain and Consul (1971, and includes as a special case the negative binomial distribution of order k, type I, of Philippou et al. (1983. This new distribution gives rise in the limit to generalized logarithmic and Borel-Tanner distributions and, by compounding, to the generalized PÃƒÂ³lya distribution of the same order and type. Limiting cases are considered and an application to observed data is presented.
零膨胀负二项回归模型的推广与费率厘定%Generalization of zero-inflated negative binomial regression model and ratemaking
Institute of Scientific and Technical Information of China (English)
徐昕; 袁卫; 孟生旺
2012-01-01
When the claim numbers appear to be over-dispersed in ratemaking, negative binomial regression model will be usually applied. However, it is also possible that the claim numbers may be zero-inflated, and then the negative binomial regression is not suitable for those data. The paper makes generalization of zero-inflated negative binomial distribution based on traditional ones to deal with the over-dispersed and zero-inflated data simultaneously. At the end of the paper, the extended model is applied to a data set of automobile insurance loss and the result shows that the goodness-of-fit can be effectively improved.%在费率厘定中,当索赔次数数据存在过离散(over-dispersion)特征时,通常会采用负二项回归模型,但当索赔数据中同时又出现零膨胀(zero-inflated)问题时,负二项回归模型不再适合对这样的数据进行分析.在传统的零膨胀负二项回归模型为基础,并将其推广到更为一般的形式,同时利用解决费率厘定中出现的既有过离散又有零膨胀的问题.通过对一组汽车损失数据的拟合,推广后的零膨胀负二项回归模型有效地改善了拟合效果.
Energy Technology Data Exchange (ETDEWEB)
Sigeti, David E. [Los Alamos National Laboratory; Pelak, Robert A. [Los Alamos National Laboratory
2012-09-11
We present a Bayesian statistical methodology for identifying improvement in predictive simulations, including an analysis of the number of (presumably expensive) simulations that will need to be made in order to establish with a given level of confidence that an improvement has been observed. Our analysis assumes the ability to predict (or postdict) the same experiments with legacy and new simulation codes and uses a simple binomial model for the probability, {theta}, that, in an experiment chosen at random, the new code will provide a better prediction than the old. This model makes it possible to do statistical analysis with an absolute minimum of assumptions about the statistics of the quantities involved, at the price of discarding some potentially important information in the data. In particular, the analysis depends only on whether or not the new code predicts better than the old in any given experiment, and not on the magnitude of the improvement. We show how the posterior distribution for {theta} may be used, in a kind of Bayesian hypothesis testing, both to decide if an improvement has been observed and to quantify our confidence in that decision. We quantify the predictive probability that should be assigned, prior to taking any data, to the possibility of achieving a given level of confidence, as a function of sample size. We show how this predictive probability depends on the true value of {theta} and, in particular, how there will always be a region around {theta} = 1/2 where it is highly improbable that we will be able to identify an improvement in predictive capability, although the width of this region will shrink to zero as the sample size goes to infinity. We show how the posterior standard deviation may be used, as a kind of 'plan B metric' in the case that the analysis shows that {theta} is close to 1/2 and argue that such a plan B should generally be part of hypothesis testing. All the analysis presented in the paper is done with a
Generazio, Edward R.
2011-01-01
The capability of an inspection system is established by applications of various methodologies to determine the probability of detection (POD). One accepted metric of an adequate inspection system is that for a minimum flaw size and all greater flaw sizes, there is 0.90 probability of detection with 95% confidence (90/95 POD). Directed design of experiments for probability of detection (DOEPOD) has been developed to provide an efficient and accurate methodology that yields estimates of POD and confidence bounds for both Hit-Miss or signal amplitude testing, where signal amplitudes are reduced to Hit-Miss by using a signal threshold Directed DOEPOD uses a nonparametric approach for the analysis or inspection data that does require any assumptions about the particular functional form of a POD function. The DOEPOD procedure identifies, for a given sample set whether or not the minimum requirement of 0.90 probability of detection with 95% confidence is demonstrated for a minimum flaw size and for all greater flaw sizes (90/95 POD). The DOEPOD procedures are sequentially executed in order to minimize the number of samples needed to demonstrate that there is a 90/95 POD lower confidence bound at a given flaw size and that the POD is monotonic for flaw sizes exceeding that 90/95 POD flaw size. The conservativeness of the DOEPOD methodology results is discussed. Validated guidelines for binomial estimation of POD for fracture critical inspection are established.
Binomial tau-leap spatial stochastic simulation algorithm for applications in chemical kinetics.
Marquez-Lago, Tatiana T; Burrage, Kevin
2007-09-14
In cell biology, cell signaling pathway problems are often tackled with deterministic temporal models, well mixed stochastic simulators, and/or hybrid methods. But, in fact, three dimensional stochastic spatial modeling of reactions happening inside the cell is needed in order to fully understand these cell signaling pathways. This is because noise effects, low molecular concentrations, and spatial heterogeneity can all affect the cellular dynamics. However, there are ways in which important effects can be accounted without going to the extent of using highly resolved spatial simulators (such as single-particle software), hence reducing the overall computation time significantly. We present a new coarse grained modified version of the next subvolume method that allows the user to consider both diffusion and reaction events in relatively long simulation time spans as compared with the original method and other commonly used fully stochastic computational methods. Benchmarking of the simulation algorithm was performed through comparison with the next subvolume method and well mixed models (MATLAB), as well as stochastic particle reaction and transport simulations (CHEMCELL, Sandia National Laboratories). Additionally, we construct a model based on a set of chemical reactions in the epidermal growth factor receptor pathway. For this particular application and a bistable chemical system example, we analyze and outline the advantages of our presented binomial tau-leap spatial stochastic simulation algorithm, in terms of efficiency and accuracy, in scenarios of both molecular homogeneity and heterogeneity. PMID:17867731
The overlooked potential of Generalized Linear Models in astronomy, I: Binomial regression
de Souza, R. S.; Cameron, E.; Killedar, M.; Hilbe, J.; Vilalta, R.; Maio, U.; Biffi, V.; Ciardi, B.; Riggs, J. D.
2015-09-01
Revealing hidden patterns in astronomical data is often the path to fundamental scientific breakthroughs; meanwhile the complexity of scientific enquiry increases as more subtle relationships are sought. Contemporary data analysis problems often elude the capabilities of classical statistical techniques, suggesting the use of cutting edge statistical methods. In this light, astronomers have overlooked a whole family of statistical techniques for exploratory data analysis and robust regression, the so-called Generalized Linear Models (GLMs). In this paper-the first in a series aimed at illustrating the power of these methods in astronomical applications-we elucidate the potential of a particular class of GLMs for handling binary/binomial data, the so-called logit and probit regression techniques, from both a maximum likelihood and a Bayesian perspective. As a case in point, we present the use of these GLMs to explore the conditions of star formation activity and metal enrichment in primordial minihaloes from cosmological hydro-simulations including detailed chemistry, gas physics, and stellar feedback. We predict that for a dark mini-halo with metallicity ≈ 1.3 × 10-4Z⨀, an increase of 1.2 × 10-2 in the gas molecular fraction, increases the probability of star formation occurrence by a factor of 75%. Finally, we highlight the use of receiver operating characteristic curves as a diagnostic for binary classifiers, and ultimately we use these to demonstrate the competitive predictive performance of GLMs against the popular technique of artificial neural networks.
Free braided differential calculus, braided binomial theorem and the braided exponential map
Majid, S
1993-01-01
Braided differential operators $\\del^i$ are obtained by differentiating the addition law on the braided covector spaces introduced previously (such as the braided addition law on the quantum plane). These are affiliated to a Yang-Baxter matrix $R$. The quantum eigenfunctions $\\exp_R(\\vecx|\\vecv)$ of the $\\del^i$ (braided-plane waves) are introduced in the free case where the position components $x_i$ are totally non-commuting. We prove a braided $R$-binomial theorem and a braided-Taylors theorem $\\exp_R(\\veca|\\del)f(\\vecx)=f(\\veca+\\vecx)$. These various results precisely generalise to a generic $R$-matrix (and hence to $n$-dimensions) the well-known properties of the usual 1-dimensional $q$-differential and $q$-exponential. As a related application, we show that the q-Heisenberg algebra $px-qxp=1$ is a braided semidirect product $\\C[x]\\cocross \\C[p]$ of the braided line acting on itself (a braided Weyl algebra). Similarly for its generalization to an arbitrary $R$-matrix.
The binomial work-health in the transit of Curitiba city.
Tokars, Eunice; Moro, Antonio Renato Pereira; Cruz, Roberto Moraes
2012-01-01
The working activity in traffic of the big cities complex interacts with the environment is often in unsafe and unhealthy imbalance favoring the binomial work - health. The aim of this paper was to analyze the relationship between work and health of taxi drivers in Curitiba, Brazil. This cross-sectional observational study with 206 individuals used a questionnaire on the organization's profile and perception of the environment and direct observation of work. It was found that the majority are male, aged between 26 and 49 years and has a high school degree. They are sedentary, like making a journey from 8 to 12 hours. They consider a stressful profession, related low back pain and are concerned about safety and accidents. 40% are smokers and consume alcoholic drink and 65% do not have or do not use devices of comfort. Risk factors present in the daily taxi constraints cause physical, cognitive and organizational and can affect your performance. It is concluded that the taxi drivers must change the unhealthy lifestyle, requiring a more efficient management of government authorities for this work is healthy and safe for all involved. PMID:22317175
Manu Batra; Aasim Farooq Shah; Prashant Rajput; Ishrat Aasim Shah
2016-01-01
Context: Dental caries among children has been described as a pandemic disease with a multifactorial nature. Various sociodemographic factors and oral hygiene practices are commonly tested for their influence on dental caries. In recent years, a recent statistical model that allows for covariate adjustment has been developed and is commonly referred zero-inflated negative binomial (ZINB) models. Aim: To compare the fit of the two models, the conventional linear regression (LR) model and ZINB ...
Energy Technology Data Exchange (ETDEWEB)
Mouayn, Zouhaïr, E-mail: mouayn@fstbm.ac.ma [Faculty of Sciences and Technics (Morocco)
2014-12-15
While considering a class of generalized negative binomial states, we verify that the basic minimum properties for these states to be considered as coherent states are satisfied. We particularize them for the case of the Hamiltonian of the isotonic oscillator and we determine the corresponding Husimi’s Q-function. This function is then exploited to obtain a lower bound for the thermodynamical potential of the Hamiltonian by applying a Berezin-Lieb inequality.
Football goal distributions and extremal statistics
Greenhough, J.; Birch, P. C.; Chapman, S. C.; Rowlands, G.
2002-12-01
We analyse the distributions of the number of goals scored by home teams, away teams, and the total scored in the match, in domestic football games from 169 countries between 1999 and 2001. The probability density functions (PDFs) of goals scored are too heavy-tailed to be fitted over their entire ranges by Poisson or negative binomial distributions which would be expected for uncorrelated processes. Log-normal distributions cannot include zero scores and here we find that the PDFs are consistent with those arising from extremal statistics. In addition, we show that it is sufficient to model English top division and FA Cup matches in the seasons of 1970/71-2000/01 on Poisson or negative binomial distributions, as reported in analyses of earlier seasons, and that these are not consistent with extremal statistics.
Institute of Scientific and Technical Information of China (English)
徐昕; 郭念国
2011-01-01
The paper discusses two types of distribution forms zero-inflated negative binomial regression models, and applies the two models to a set of actual automobile insurance loss data. The results show that the two types of zero-inflated negative binomial regression models can improve the goodness-of-fit effectively than the common claim frequency models when the loss data is zero-inflated.%讨论了两种分布形式的零膨胀负二项回归模型，并应用一组实际汽车保险损失数据对两类模型进行了实证比较．结果表明，对于具有零膨胀特征的损失数据，零膨胀负二项回归模型的拟合结果优于普通索赔频率回归模型．
Universality of multiplicity distribution in proton-proton and electron-positron collisions
Bzdak, Adam
2015-01-01
It is argued that the multiplicity distribution in proton-proton ($pp$) collisions, which is often parameterized by the negative binomial distribution, results from the multiplicity distribution measured in electron-positron ($e^{+}e^{-}$) collisions, once the fluctuating energy carried by two leading protons in $pp$ is taken into account.
Optimal Transportation-entropy Inequalities for Several Usual Distributions on R
Institute of Scientific and Technical Information of China (English)
Wei LIU
2011-01-01
In this paper,based on the recent results of Gozlan and Léonard we give optimal transportationentropy inequalities for several usual distributions on R,such as Bernoulli,Binomial,Poisson,Gamma distributions and infinitely divisible distributions with positive or negative jumps.
Kondo, Yumi; Zhao, Yinshan; Petkau, John
2015-06-15
We develop a new modeling approach to enhance a recently proposed method to detect increases of contrast-enhancing lesions (CELs) on repeated magnetic resonance imaging, which have been used as an indicator for potential adverse events in multiple sclerosis clinical trials. The method signals patients with unusual increases in CEL activity by estimating the probability of observing CEL counts as large as those observed on a patient's recent scans conditional on the patient's CEL counts on previous scans. This conditional probability index (CPI), computed based on a mixed-effect negative binomial regression model, can vary substantially depending on the choice of distribution for the patient-specific random effects. Therefore, we relax this parametric assumption to model the random effects with an infinite mixture of beta distributions, using the Dirichlet process, which effectively allows any form of distribution. To our knowledge, no previous literature considers a mixed-effect regression for longitudinal count variables where the random effect is modeled with a Dirichlet process mixture. As our inference is in the Bayesian framework, we adopt a meta-analytic approach to develop an informative prior based on previous clinical trials. This is particularly helpful at the early stages of trials when less data are available. Our enhanced method is illustrated with CEL data from 10 previous multiple sclerosis clinical trials. Our simulation study shows that our procedure estimates the CPI more accurately than parametric alternatives when the patient-specific random effect distribution is misspecified and that an informative prior improves the accuracy of the CPI estimates. PMID:25784219
Majumdar, Arunabha; Witte, John S.; Ghosh, Saurabh
2016-01-01
Binary phenotypes commonly arise due to multiple underlying quantitative precursors. Genetic variants may impact multiple traits in a pleiotropic manner. Hence, simultaneously analyzing such correlated traits may be more powerful than analyzing individual traits. Various genotype-level methods, e.g. MultiPhen [O'Reilly et al., 2012], have been developed to identify genetic factors underlying a multivariate phenotype. For univariate phenotypes, the usefulness and applicability of allele-level tests have been investigated. The test of allele frequency difference among cases and controls is commonly used for mapping case-control association. However, allelic methods for multivariate association mapping have not been studied much. We explore two allelic tests of multivariate association: one using a Binomial regression model based on inverted regression of genotype on phenotype (BAMP), and the other employing the Mahalanobis distance between two sample means of the multivariate phenotype vector for two alleles at a SNP (DAMP). These methods can incorporate both discrete and continuous phenotypes. Some theoretical properties for BAMP are studied. Using simulations, the power of the methods for detecting multivariate association are compared with the genotype-level test MultiPhen. The allelic tests yield marginally higher power than MultiPhen for multivariate phenotypes. For one/two binary traits under recessive mode of inheritance, allelic tests are found substantially more powerful. All three tests are applied to two real data and the results offer some support for the simulation study. Since the allelic approaches assume Hardy-Weinberg Equilibrium (HWE), we propose a hybrid approach for testing multivariate association that implements MultiPhen when HWE is violated and BAMP otherwise. PMID:26493781
Some Large Deviation Results for Generalized Compound Binomial Risk Models%广义复合二项风险模型的若干大偏差结果
Institute of Scientific and Technical Information of China (English)
孔繁超; 赵朋
2009-01-01
This paper is a further investigation of large deviation for partial and random sums of random variables, where {X_n, n≥ 1} is non-negative independent identically distributed random variables with a common heavy-tailed distribution function F on the real line R and finite mean μ∈ R. {N(n),n≥ 0} is a binomial process with a parameter p ∈ (0, 1) and independent of {X_n,n≥1}; {M(n),n≥0} is a Poisson process with intensity λ > 0, S_n=∑~(N(n))_(i=1) X_i-cM(n). Suppose F ∈ C, we futher extend and improve some large deviation results. These results can apply to certain problems in insurance and finance.
Naznin, Farhana; Currie, Graham; Logan, David; Sarvi, Majid
2016-07-01
Safety is a key concern in the design, operation and development of light rail systems including trams or streetcars as they impose crash risks on road users in terms of crash frequency and severity. The aim of this study is to identify key traffic, transit and route factors that influence tram-involved crash frequencies along tram route sections in Melbourne. A random effects negative binomial (RENB) regression model was developed to analyze crash frequency data obtained from Yarra Trams, the tram operator in Melbourne. The RENB modelling approach can account for spatial and temporal variations within observation groups in panel count data structures by assuming that group specific effects are randomly distributed across locations. The results identify many significant factors effecting tram-involved crash frequency including tram service frequency (2.71), tram stop spacing (-0.42), tram route section length (0.31), tram signal priority (-0.25), general traffic volume (0.18), tram lane priority (-0.15) and ratio of platform tram stops (-0.09). Findings provide useful insights on route section level tram-involved crashes in an urban tram or streetcar operating environment. The method described represents a useful planning tool for transit agencies hoping to improve safety performance. PMID:27035395
Statistical distributions of earthquake numbers: consequence of branching process
Kagan, Yan Y.
2010-01-01
We discuss various statistical distributions of earthquake numbers. Previously we derived several discrete distributions to describe earthquake numbers for the branching model of earthquake occurrence: these distributions are the Poisson, geometric, logarithmic, and the negative binomial (NBD). The theoretical model is the `birth and immigration' population process. The first three distributions above can be considered special cases of the NBD. In particular, a point branching process along t...
Distance distribution in configuration-model networks
Nitzan, Mor; Katzav, Eytan; Kühn, Reimer; Biham, Ofer
2016-06-01
We present analytical results for the distribution of shortest path lengths between random pairs of nodes in configuration model networks. The results, which are based on recursion equations, are shown to be in good agreement with numerical simulations for networks with degenerate, binomial, and power-law degree distributions. The mean, mode, and variance of the distribution of shortest path lengths are also evaluated. These results provide expressions for central measures and dispersion measures of the distribution of shortest path lengths in terms of moments of the degree distribution, illuminating the connection between the two distributions.
James, William H
2009-01-01
Abstract It is 100 years since Gini noted that in some samples of litters of mice and rabbits, the variances of the distributions of the combinations of the sexes are sub-binomial. In other words, in contrast with binomial expectation, there are too many litters in which the sexes are equally balanced, and there are too few unisexual litters. In the intervening years, this finding has been replicated in a number of further species, but no explanation has become established. Potenti...
International Nuclear Information System (INIS)
In the solid state nuclear track detectors of chemically etched type, nuclear tracks with center-to-center neighborhood of distance shorter than two times the radius of tracks will emerge as overlapping tracks. Track overlapping in this type of detectors causes tracks count losses and it becomes rather severe in high track densities. Therefore, tracks counting in this condition should include a correction factor for count losses of different tracks overlapping orders since a number of overlapping tracks may be counted as one track. Another aspect of the problem is the cases where imaging the whole area of the detector and counting all tracks are not possible. In these conditions a statistical generalization method is desired to be applicable in counting a segmented area of the detector and the results can be generalized to the whole surface of the detector. Also there is a challenge in counting the tracks in densely overlapped tracks because not sufficient geometrical or contextual information are available. It this paper we present a statistical counting method which gives the user a relation between the tracks overlapping probabilities on a segmented area of the detector surface and the total number of tracks. To apply the proposed method one can estimate the total number of tracks on a solid state detector of arbitrary shape and dimensions by approximating the tracks averaged area, whole detector surface area and some orders of tracks overlapping probabilities. It will be shown that this method is applicable in high and ultra high density tracks images and the count loss error can be enervated using a statistical generalization approach. - Highlights: • A correction factor for count losses of different tracks overlapping orders. • For the cases imaging the whole area of the detector is not possible. • Presenting a statistical generalization method for segmented areas. • Giving a relation between the tracks overlapping probabilities and the total tracks
Directory of Open Access Journals (Sweden)
Paweł Mielcarz
2007-06-01
Full Text Available The article presents a case study of valuation of real options included in a investment project. The main goal of the article is to present the calculation and methodological issues of application the methodology for real option valuation. In order to do it there are used the binomial model and Market Asset Declaimer methodology. The project presented in the article concerns the introduction of radio station to a new market. It includes two valuable real options: to abandon the project and to expand.
Shirazi, Mohammadali; Lord, Dominique; Dhavala, Soma Sekhar; Geedipally, Srinivas Reddy
2016-06-01
Crash data can often be characterized by over-dispersion, heavy (long) tail and many observations with the value zero. Over the last few years, a small number of researchers have started developing and applying novel and innovative multi-parameter models to analyze such data. These multi-parameter models have been proposed for overcoming the limitations of the traditional negative binomial (NB) model, which cannot handle this kind of data efficiently. The research documented in this paper continues the work related to multi-parameter models. The objective of this paper is to document the development and application of a flexible NB generalized linear model with randomly distributed mixed effects characterized by the Dirichlet process (NB-DP) to model crash data. The objective of the study was accomplished using two datasets. The new model was compared to the NB and the recently introduced model based on the mixture of the NB and Lindley (NB-L) distributions. Overall, the research study shows that the NB-DP model offers a better performance than the NB model once data are over-dispersed and have a heavy tail. The NB-DP performed better than the NB-L when the dataset has a heavy tail, but a smaller percentage of zeros. However, both models performed similarly when the dataset contained a large amount of zeros. In addition to a greater flexibility, the NB-DP provides a clustering by-product that allows the safety analyst to better understand the characteristics of the data, such as the identification of outliers and sources of dispersion. PMID:26945472
Understanding the negative binomial multiplicity fluctuations in relativistic heavy ion collisions
Xu, Hao-jie
2016-01-01
By deriving a general expression for multiplicity distribution (a conditional probability distribution) in statistical model, we demonstrate the mismatches between experimental measurements and previous theoretical calculations on multiplicity fluctuations. From the corrected formula, we develop an improved baseline measure for multiplicity distribution under Poisson approximation in statistical model to replace the traditional Poisson expectations. We find that the ratio of the mean multipli...
A Poisson Mixed Model with Nonnormal Random Effect Distribution
Fabio, Lizandra C.; Gilberto A. Paula; Castro, Mario
2011-01-01
We propose in this paper a random intercept Poisson model in which the random effect distribution is assumed to follow a generalized log-gamma (GLG) distribution. We derive the first two moments for the marginal distribution as well as the intraclass correlation. Even though numerical integration methods are in general required for deriving the marginal models, we obtain the multivariate negative binomial model for a particular parameter setting of the hierarchical model. An iterative process...
How to retrieve additional information from the multiplicity distributions
Wilk, Grzegorz; Włodarczyk, Zbigniew
2016-01-01
Multiplicity distributions $P(N)$ measured in multiparticle production processes are most frequently described by the Negative Binomial Distribution (NBD). However, with increasing collision energy some systematic discrepancies become more and more apparent. They are usually attributed to the possible multi-source structure of the production process and described using a multi-NBD form of the multiplicity distribution. We investigate the possibility of keeping a single NBD but with its parame...
Self-affirmation model for football goal distributions
Bittner, Elmar; Nussbaumer, Andreas; Janke, Wolfhard; Weigel, Martin
2007-01-01
Analyzing football score data with statistical techniques, we investigate how the highly co-operative nature of the game is reflected in averaged properties such as the distributions of scored goals for the home and away teams. It turns out that in particular the tails of the distributions are not well described by independent Bernoulli trials, but rather well modeled by negative binomial or generalized extreme value distributions. To understand this behavior from first principles, we suggest...
Generazio, Edward R.
2014-01-01
Unknown risks are introduced into failure critical systems when probability of detection (POD) capabilities are accepted without a complete understanding of the statistical method applied and the interpretation of the statistical results. The presence of this risk in the nondestructive evaluation (NDE) community is revealed in common statements about POD. These statements are often interpreted in a variety of ways and therefore, the very existence of the statements identifies the need for a more comprehensive understanding of POD methodologies. Statistical methodologies have data requirements to be met, procedures to be followed, and requirements for validation or demonstration of adequacy of the POD estimates. Risks are further enhanced due to the wide range of statistical methodologies used for determining the POD capability. Receiver/Relative Operating Characteristics (ROC) Display, simple binomial, logistic regression, and Bayes' rule POD methodologies are widely used in determining POD capability. This work focuses on Hit-Miss data to reveal the framework of the interrelationships between Receiver/Relative Operating Characteristics Display, simple binomial, logistic regression, and Bayes' Rule methodologies as they are applied to POD. Knowledge of these interrelationships leads to an intuitive and global understanding of the statistical data, procedural and validation requirements for establishing credible POD estimates.
How does the Shift-insertion sort behave when the sorting elements follow a Normal distribution?
Pal, Mita; Mahanti, N C
2012-01-01
The present paper examines the behavior of Shift-insertion sort (insertion sort with shifting) for normal distribution inputs and is in continuation of our earlier work on this new algorithm for discrete distribution inputs, namely, negative binomial. Shift insertion sort is found more sensitive for main effects but not for all interaction effects compared to conventional insertion sort.
Some Instructional Issues in Hypergeometric Distribution
Directory of Open Access Journals (Sweden)
Anwar H. Joarder
2012-07-01
Full Text Available 800x600 Normal 0 false false false EN-US X-NONE X-NONE A brief introduction to sampling without replacement is presented. We represent the probability of a sample outcome in sampling without replacement from a finite population by three equivalent forms involving permutation and combination. Then it is used to calculate the probability of any number of successes in a given sample. The resulting forms are equivalent to the well known mass function of the hypergeometric distribution. Vandermonde’s identity readily justifies different forms of the mass function. One of the new form of the mass function embodies binomial coefficient showing much resemblance to that of binomial distribution. It also yields some interesting identities. Some other related issues are discussed.
Multiplicity distributions in a thermodynamical model of hadron production in e+e- collisions
Becattini, F; Lupia, S
1996-01-01
Predictions of a thermodynamical model of hadron production for multiplicity distributions in e^+e^- annihilations at LEP and PEP-PETRA centre of mass energies are shown. The production process is described as a two-step process in which primary hadrons emitted from the thermal source decay into final observable particles. The final charged tracks multiplicity distributions turn out to be of Negative Binomial type and are in quite good agreement with experimental observations. The average number of clans calculated from fitted Negative Binomial coincides with the average number of primary hadrons predicted by the thermodynamical model, suggesting that clans should be identified with primary hadrons.
Statistical Yield Modeling for IC Manufacture Hierarchical Fault Distributions
Bogdanov, Y I; Dshkhunyan, V L; Bogdanov, Yu.I.
2003-01-01
A hierarchical approach to the construction of compound distributions for process-induced faults in IC manufacture is proposed. Within this framework, the negative binomial distribution and the compound binomial distribution are treated as level-1 models. The hierarchical approach to fault distribution offers an integrated picture of how fault density varies from region to region within a wafer, from wafer to wafer within a batch, and so on. A theory of compound-distribution hierarchies is developed by means of generating functions. With respect to applications, hierarchies of yield means and yield probability-density functions are considered and an in-process measure of yield loss is introduced. It is shown that the hierarchical approach naturally embraces the Bayesian approach.
Directory of Open Access Journals (Sweden)
Marcelo Angelo Cirillo
2010-07-01
Full Text Available A inferencia estatistica em populacoes binomiais contaminadas esta sujeita a erros grosseiros de estimacao, uma vez que as amostras nao sao identicamente distribuidas. Por esse problema, este trabalho tem por objetivo determinar qual a melhor constante de afinidade (c1 que proporcione melhor desempenho em um estimador pertencente a classedos estimadores-E. Com esse proposito, neste trabalho, foi utilizada a metodologia, considerando-se o metodo de simulacao Monte Carlo, no qual diferentes configuracoes descritas pela combinacao de valores parametricos, niveis de contaminacao e tamanhos de amostra foram avaliados. Concluiu-se que, para alta probabilidade de mistura (ƒÁ = 0,40, recomenda-se assumir c1 = 0,1 nas situacoes de grandes amostras (n = 50 e n = 80. The statistical inference in binomial population is subject to gross errors of estimate, as the samples are not identically distributed. Due to this problem, this work aims to determine which is the best affinity constant (c1 that provides the best performance in the estimator, belonging to the class of E-estimators. With that purpose, the methodology used in this work was applied considering the Monte Carlo simulation method, in which different configurations described by combination of parametric values, levels of contamination and sample sizes were appraised. It was concluded that for the high probability of contamination (ƒÁ = 0.40, c1 = 0.1 is recommended in cases with large samples (n = 50 and n = 80.
The Influence of Multiplicity Distribution on the Erraticity Behavior of Multiparticle Production
Zhixu, Liu; Jinghua, Fu; Lianshou, Liu
1999-01-01
The origin of the erraticity behaviour observed recently in the experiment is studied in some detail. The negative-binomial distribution is used to fit the experimental multiplicity distribution. It is shown that, with the multiplicity distribution taken into account, the experimentally observed erraticity behaviour can be well reproduced using a flat probability distribution. The dependence of erraticity behaviour on the width of multiplicity distribution is studied.
Institute of Scientific and Technical Information of China (English)
索瑞鑫; 仇玉兰; 王彤
2012-01-01
目的 通过模拟研究对几种可用于小样本微核数据统计分析的方法进行讨论,为小样本微核数据的分析提供科学依据.方法 用R软件进行编程模拟来估计不同参数下不同分析方法的Ⅰ类错误和检验功效.结果 Poisson精确概率法、Fisher精确概率法、负二项精确概率法、t检验及其变换、确切概率秩和检验的检验功效和Ⅰ型错误各不相同,其检验功效随δ和动物数n的增大而增大.其中Poisson精确概率法、Fisher精确概率法、负二项精确概率法的检验功效较高,但总体来自于负二项分布时,Poisson精确概率法、Fisher精确概率法的Ⅰ型错误较大,而负二项精确概率法Ⅰ型错误较小.结论 在小样本微核数据分析中负二项精确概率法具有检验功效较高且犯Ⅰ型错误概率小的优越性.%Objective To explore the statistical analysis method of small-sample micronuclei data by simulation studies. Methods We simulated small-sample micronuclei data,then compared the size and power of the test methods in literature for the micronuclei assay analysis. Results Compared the type I error and statistical power of several different small-sample anaysis approading for micronuclei data, etatistical analysis methods , such as Poisson exact test, Fisher exact test, Negative Binomial Exact Test,t test,t test after transformation,rank sum exact test,were considered. The power of tests increase with 8 and n. Statistical power of Poisson exact test was the highest. Fisher exact test and Negative Binomial Exact Test were lower than Poisson exact test,and higher than other statistical analysis methods. But under negative binomial distribution, type Ⅰ error was large in Poisson exact test and Fisher exact test, while it was small in Negative Binomial Exact Test. Conclusion The power of the Negative Binomial Exact was higher in spite of the lower type I error.
考虑投资的双复合二项风险模型的破产概率%Ruin Probabilities of a Double Compound Binomial Risk Model with Investment
Institute of Scientific and Technical Information of China (English)
乔克林; 侯致武
2011-01-01
在考虑投资收益的基础上,假定保费收取次数和理赔次数均服从二项分布,讨论了投资收益率为常数和一随机序列且保费也为一随机序列情形下风险模型的破产概率,推导出了该模型的破产概率表达式及上界;并在投资收益正态假定下对两类双复合二项风险模型的调节系数及破产概率上界进行了比较,进而说明调节系数是综合反映模型风险水平的一个重要因子。%Based on investment income,it is supposed that the premium Collection number and the claim number both obey the binomial distribution.The investment return rate as the constant and a random sequence and insurance is for a random sequence case risk model for the ruin probability is discussed.The model for the ruin probability expression and upper bound are deduced.The adjustment coefficient and upper boundary of the ruin probability for two kinds of double compound binomial risk model in the investment returns to normal assumption are compared,and then explain adjustment coefficient is the comprehensive reflection of the level of risk model of an important factor.
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Manu Batra
2016-01-01
Full Text Available Context: Dental caries among children has been described as a pandemic disease with a multifactorial nature. Various sociodemographic factors and oral hygiene practices are commonly tested for their influence on dental caries. In recent years, a recent statistical model that allows for covariate adjustment has been developed and is commonly referred zero-inflated negative binomial (ZINB models. Aim: To compare the fit of the two models, the conventional linear regression (LR model and ZINB model to assess the risk factors associated with dental caries. Materials and Methods: A cross-sectional survey was conducted on 1138 12-year-old school children in Moradabad Town, Uttar Pradesh during months of February-August 2014. Selected participants were interviewed using a questionnaire. Dental caries was assessed by recording decayed, missing, or filled teeth (DMFT index. Statistical Analysis Used: To assess the risk factor associated with dental caries in children, two approaches have been applied - LR model and ZINB model. Results: The prevalence of caries-free subjects was 24.1%, and mean DMFT was 3.4 ± 1.8. In LR model, all the variables were statistically significant. Whereas in ZINB model, negative binomial part showed place of residence, father′s education level, tooth brushing frequency, and dental visit statistically significant implying that the degree of being caries-free (DMFT = 0 increases for group of children who are living in urban, whose father is university pass out, who brushes twice a day and if have ever visited a dentist. Conclusion: The current study report that the LR model is a poorly fitted model and may lead to spurious conclusions whereas ZINB model has shown better goodness of fit (Akaike information criterion values - LR: 3.94; ZINB: 2.39 and can be preferred if high variance and number of an excess of zeroes are present.
Testing QCD Predictions for Multiplicity Distributions at HERA
Hegyi, S.
1996-01-01
On the basis of a recently introduced generalization of the negative binomial distribution the influence of higher-order perturbative QCD effects on multiplicity fluctuations are studied for deep inelastic e^+p scattering at HERA energies. It is found that the multiplicity distributions measured by the H1 Collaboration indicate violation of infinite divisibility in agreement with pQCD calculations. Attention is called to future experimental analysis of combinants whose nontrivial sign-changin...
Football fever: goal distributions and non-Gaussian statistics
Bittner, Elmar; Nussbaumer, Andreas; Janke, Wolfhard; Weigel, Martin
2006-01-01
Analyzing football score data with statistical techniques, we investigate how the not purely random, but highly co-operative nature of the game is reflected in averaged properties such as the probability distributions of scored goals for the home and away teams. As it turns out, especially the tails of the distributions are not well described by the Poissonian or binomial model resulting from the assumption of uncorrelated random events. Instead, a good effective description of the data is pr...
Some Properties of the Generalized Stuttering Poisson Distribution and its Applications
Zhang, Huiming; Chu, Lili; Diao, Yu
2012-01-01
Based on the probability generating function of stuttering Poisson distribution (SPD), this paper considers some equivalent propositions of SPD. From this, we show that some distributions in the application of non-life insurance actuarial science are SPD, such as negative binomial distribution, compound Poisson distribution etc.. By weakening condition of equivalent propositions of SPD, we define the generalized SPD. We consider cumulant estimation of generalized SPD's parameters. As an appli...
Football fever: goal distributions and non-Gaussian statistics
Bittner, E; Janke, W; Weigel, M; Bittner, Elmar; Nussbaumer, Andreas; Janke, Wolfhard; Weigel, Martin
2006-01-01
Analyzing football score data with statistical techniques, we investigate how the not purely random, but highly co-operative nature of the game is reflected in averaged properties such as the probability distributions of scored goals for the home and away teams. As it turns out, especially the tails of the distributions are not well described by the Poissonian or binomial model resulting from the assumption of uncorrelated random events. Instead, a good effective description of the data is provided by less basic distributions such as the negative binomial one or the probability densities of extreme value statistics. To understand this behavior from a microscopical point of view, however, no waiting time problem or extremal process need be invoked. Instead, modifying the Bernoulli random process underlying the Poissonian model to include a simple component of self-affirmation seems to describe the data surprisingly well and allows to understand the observed deviation from Gaussian statistics. The phenomenologi...
A comparison of methods for the analysis of binomial proportion data in behavioral research
Ferrari, Alberto; Comelli, Mario
2016-01-01
In behavioral and psychiatric research, data consisting of a per-subject proportion of "successes" and "failures" over a finite number of trials often arise. This kind of clustered binary data are usually non-normally distributed, which can cause issues with parameter estimation and predictions if the usual general linear model is applied and sample size is small. Here we studied the performances of some of the available analytic methods applicable to the analysis of proportion data; namely l...
Is extrapair mating random? On the probability distribution of extrapair young in avian broods
Brommer, Jon E.; Korsten, Peter; Bouwman, Karen A.; Berg, Mathew L.; Komdeur, Jan
2007-01-01
A dichotomy in female extrapair copulation (EPC) behavior, with some females seeking EPC and others not, is inferred if the observed distribution of extrapair young (EPY) over broods differs from a random process on the level of individual offspring (binomial, hypergeometrical, or Poisson). A review
SYVAC3 parameter distribution package
International Nuclear Information System (INIS)
SYVAC3 (Systems Variability Analysis Code, generation 3) is a computer program that implements a method called systems variability analysis to analyze the behaviour of a system in the presence of uncertainty. This method is based on simulating the system many times to determine the variation in behaviour it can exhibit. SYVAC3 specializes in systems representing the transport of contaminants, and has several features to simplify the modelling of such systems. It provides a general tool for estimating environmental impacts from the dispersal of contaminants. This report describes a software object type (a generalization of a data type) called Parameter Distribution. This object type is used in SYVAC3, and can also be used independently. Parameter Distribution has the following subtypes: beta distribution; binomial distribution; constant distribution; lognormal distribution; loguniform distribution; normal distribution; piecewise uniform distribution; Triangular distribution; and uniform distribution. Some of these distributions can be altered by correlating two parameter distribution objects. This report provides complete specifications for parameter distributions, and also explains how to use them. It should meet the needs of casual users, reviewers, and programmers who wish to add their own subtypes. (author). 30 refs., 75 tabs., 56 figs
Gastón Silverio Milanesi
2014-01-01
El trabajo tiene por objeto exponer la metodología, las ventajas y las debilidades del modelo binomial borroso de valoración de opciones reales como complemento del modelo binomial probabilístico. Para lograr lo anterior primero se presentan los modelos de opciones reales clasificados en probabilístico y borroso; luego se desarrolla el modelo binomial borroso incorporando: el método Marketed Asset Disclai- mer (MAD), rejillas binomiales borrosas y el índice pesimismo-optimismo, para es...
Energy Technology Data Exchange (ETDEWEB)
Hernandez I, S.; Ortiz C, E.; Chavez M, C., E-mail: lunitza@gmail.com [UNAM, Facultad de Ingenieria, Circuito Interior, Ciudad Universitaria, 04510 Mexico D. F. (Mexico)
2011-11-15
At the present time, is an unquestionable fact that the nuclear electrical energy is a topic of vital importance, no more because eliminates the dependence of the hydrocarbons and is friendly with the environment, but because is also a sure and reliable energy source, and represents a viable alternative before the claims in the growing demand of electricity in Mexico. Before this panorama, was intended several scenarios to elevate the capacity of electric generation of nuclear origin with a variable participation. One of the contemplated scenarios is represented by the expansion project of the nuclear power plant Laguna Verde through the addition of a third reactor that serves as detonator of an integral program that proposes the installation of more nuclear reactors in the country. Before this possible scenario, the Federal Commission of Electricity like responsible organism of supplying energy to the population should have tools that offer it the flexibility to be adapted to the possible changes that will be presented along the project and also gives a value to the risk to future. The methodology denominated Real Options, Binomial model was proposed as an evaluation tool that allows to quantify the value of the expansion proposal, demonstrating the feasibility of the project through a periodic visualization of their evolution, all with the objective of supplying a financial analysis that serves as base and justification before the evident apogee of the nuclear energy that will be presented in future years. (Author)
On a Generalisation of Uniform Distribution and its Properties
Directory of Open Access Journals (Sweden)
K. Jayakumar
2016-03-01
Full Text Available Nadarajah et al.(2013 introduced a family life time models using truncated negative binomial distribution and derived some properties of the family of distributions. It is a generalization of Marshall-Olkin family of distributions. In this paper, we introduce Generalized Uniform Distribution (GUD using the approach of Nadarajah et al.(2013. The shape properties of density function and hazard function are discussed. The expression for moments, order statistics, entropies are obtained. Estimation procedure is also discussed.The GDU introduced here is a generalization of the Marshall-Olkin extended uniform distribution studied in Jose and Krishna(2011.
International Nuclear Information System (INIS)
At the present time, is an unquestionable fact that the nuclear electrical energy is a topic of vital importance, no more because eliminates the dependence of the hydrocarbons and is friendly with the environment, but because is also a sure and reliable energy source, and represents a viable alternative before the claims in the growing demand of electricity in Mexico. Before this panorama, was intended several scenarios to elevate the capacity of electric generation of nuclear origin with a variable participation. One of the contemplated scenarios is represented by the expansion project of the nuclear power plant Laguna Verde through the addition of a third reactor that serves as detonator of an integral program that proposes the installation of more nuclear reactors in the country. Before this possible scenario, the Federal Commission of Electricity like responsible organism of supplying energy to the population should have tools that offer it the flexibility to be adapted to the possible changes that will be presented along the project and also gives a value to the risk to future. The methodology denominated Real Options, Binomial model was proposed as an evaluation tool that allows to quantify the value of the expansion proposal, demonstrating the feasibility of the project through a periodic visualization of their evolution, all with the objective of supplying a financial analysis that serves as base and justification before the evident apogee of the nuclear energy that will be presented in future years. (Author)
Institute of Scientific and Technical Information of China (English)
姜培华; 范国良
2013-01-01
建立了一类系统受冲击损伤的数学模型，在系统工作环境承受冲击损伤的到来服从负二项分布、冲击引起的损伤服从指数分布的条件下，讨论了系统损伤未达到危险临界值的概率、平均损伤、引起系统失效的平均冲击次数及系统失效率等相关可靠性指标。%Established a mathematical model of system impact damage.Under the condition that system working environment absorbing the coming shocks obeys negative binomial distribution and impact damage obeys the index distribution,discussed the related reliability index of the probability of risk threshold of the system,the average damage,the mean number of shocks caused the system failure and the efficiency of system losses.
Directory of Open Access Journals (Sweden)
Gastón Silverio Milanesi
2013-01-01
Full Text Available El trabajo propone un modelo de valoración de opciones reales con base en el modelo binomial utilizando la transformación de Edgeworth (Rubinstein, 1998 para incorporar momentos estocásticos de orden superior, especialmente para ciertos tipos de organizaciones, como empresas de base tecnológica, donde no se dispone de cartera de activos financieros gemelos, comparables de mercado y procesos estocásticos no gaussianos. Primero, se presenta el desarrollo formal del modelo, luego su aplicación sobre la valuación de spin-off tecnológico universitario, sensibilizando asimetría-curtosis y exponiendo el impacto en el valor del proyecto. Finalmente, se concluye sobre limitaciones y ventajas de la propuesta de valoración que resume la simplicidad del modelo binomial e incorporando momentos de orden superior en subyacentes con procesos no normales.
Pricing American Asian options with higher moments in the underlying distribution
Lo, Keng-Hsin; Wang, Kehluh; Hsu, Ming-Feng
2009-01-01
We develop a modified Edgeworth binomial model with higher moment consideration for pricing American Asian options. With lognormal underlying distribution for benchmark comparison, our algorithm is as precise as that of Chalasani et al. [P. Chalasani, S. Jha, F. Egriboyun, A. Varikooty, A refined binomial lattice for pricing American Asian options, Rev. Derivatives Res. 3 (1) (1999) 85-105] if the number of the time steps increases. If the underlying distribution displays negative skewness and leptokurtosis as often observed for stock index returns, our estimates can work better than those in Chalasani et al. [P. Chalasani, S. Jha, F. Egriboyun, A. Varikooty, A refined binomial lattice for pricing American Asian options, Rev. Derivatives Res. 3 (1) (1999) 85-105] and are very similar to the benchmarks in Hull and White [J. Hull, A. White, Efficient procedures for valuing European and American path-dependent options, J. Derivatives 1 (Fall) (1993) 21-31]. The numerical analysis shows that our modified Edgeworth binomial model can value American Asian options with greater accuracy and speed given higher moments in their underlying distribution.
Roger MERCKEN; MOTMANS, Lisette; Houben, Ghislain
2010-01-01
This paper covers the valuation, from beginning to implementation, of a European call option on a stock using the multi-step binomial model in a risk-neutral world. The aim is to introduce this model in a simple but rather unconventional way. The usual presentation of the risk-neutral valuation, see Hull (2009), among others, relies on replicating portfolios. For most practitioners, this technique looks rather mysterious. We present a new transparent analysis requiring no replicating port...
Corona de la Fuente, Rosalinda
1999-01-01
Notas del catalogo: Introducción Se han propuesto diferentes maneras de construir intervalos de confianza para el parámetro p, de una variable aleatoria X, binomial (n,p), partiendo de que hay una correspondencia directa entre las regiones de aceptación .... Bibliografía: h. 36-37. Desc. física: 64 h. : il. ; 28 cm
Jokar-Arsanjani, Jamal; Helbich, Marco
2016-01-01
The analysis and understanding of spatial crime patterns is crucial for law enforcements to improve strategic and tactical decision-making. In this context, generalized linear models, such as count regressions, are commonly applied. These non-spatial models are challenged by spatial autocorrelation effects, contradicting fundamental model assumptions. Therefore, the purpose of this research is to present a spatially explicit approach, which combines a negative binomial model and spatial filte...
International Nuclear Information System (INIS)
A Chou-Yang Type multiplicity distribution, which consists of a stochastic (binomial) component for z=nf-nb and a nonstochastic (negative binomial) component for n=nf+nb, is used to analyse the forward-backward multiplicity correlations and the single hemisphere miultiplicity distributions for both e+e- and hadron-hadron collisions over a wide range of cms energy. Experimental data in full phase space are reasonably reproduced provided that the mean cluster size r is target-projectile and energy dependent. (orig.)
Weibull model of multiplicity distribution in hadron-hadron collisions
Dash, Sadhana; Nandi, Basanta K.; Sett, Priyanka
2016-06-01
We introduce the use of the Weibull distribution as a simple parametrization of charged particle multiplicities in hadron-hadron collisions at all available energies, ranging from ISR energies to the most recent LHC energies. In statistics, the Weibull distribution has wide applicability in natural processes that involve fragmentation processes. This provides a natural connection to the available state-of-the-art models for multiparticle production in hadron-hadron collisions, which involve QCD parton fragmentation and hadronization. The Weibull distribution describes the multiplicity data at the most recent LHC energies better than the single negative binomial distribution.
Marcelino, M C S; Barbosa, J C
2016-04-01
The psyllid Triozoida limbata (Enderlein) (Hemiptera: Triozidae) is a major pest in guava, feeding primarily on new shoots. Despite its importance, there are no studies on the spatial distribution of T. limbata on guava. Such studies are needed to establish sequential sampling plans for decision making in pest control. Thus, an experiment was carried out in a 9-year-old commercial guava orchard divided into 100 sampling units or plots. Double-sided yellow sticky traps were placed on one plant per plot (sample unit) to capture and monitor T. limbata adults from April 2011 to May 2012. To determine the insect distribution in the area, we calculated the variance-to-mean ratio index (I), the Morisita index (I δ ), Green's coefficient (Cx), and the k exponent of the negative binomial distribution. Most of the samples showed that the adults had a moderate to highly aggregated distribution. Statistical models were also used to study the pest spatial distribution by fitting the number of adults captured to the Poisson and negative binomial distributions. The negative binomial distribution model best fitted the data of the number of adult psyllids captured by the traps, which is consistent with an aggregated distribution. PMID:26597967
Rodrigues, Tatiana R; Fernandes, Marcos G; Degrande, Paulo E; Mota, Thiago A
2015-01-01
Among the options to control Alabama argillacea (Hübner, 1818) and Heliothis virescens (Fabricius, 1781) on cotton, insecticide spraying and biological control have been extensively used. The GM'Bt' cotton has been introduced as an extremely viable alternative, but it is yet not known how transgenic plants affect populations of organisms that are interrelated in an agroecosystem. For this reason, it is important to know how the spatial arrangement of pests and beneficial insect are affected, which may call for changes in the methods used for sampling these species. This study was conducted with the goal to investigate the pattern of spatial distribution of eggs of A. argillacea and H. virescens in DeltaOpal™ (non-Bt) and DP90B™ Bt cotton cultivars. Data were collected during the agricultural year 2006/2007 in two areas of 5,000 m2, located in in the district of Nova América, Caarapó municipality. In each sampling area, comprising 100 plots of 50 m2, 15 evaluations were performed on two plants per plot. The sampling consisted in counting the eggs. The aggregation index (variance/mean ratio, Morisita index and exponent k of the negative binomial distribution) and chi-square fit of the observed and expected values to the theoretical frequency distribution (Poisson, Binomial and Negative Binomial Positive), showed that in both cultivars, the eggs of these species are distributed according to the aggregate distribution model, fitting the pattern of negative binomial distribution. PMID:26628025
Smeeton, N C
1986-01-01
The Second National Morbidity Survey, conducted in England and Wales between 1970 and 1976, contains a unique body of information on episodes of mental illness experienced by individuals registered in a representative sample of general practices around the country. This information is used to construct the episode distribution among the individuals surveyed. The Poisson and negative binomial distributions are then used to model the episodes. The Poisson model gives a very poor fit but the neg...
Various Models for Pion Probability Distributions from Heavy-Ion Collisions
Mekjian, A. Z.; Schlei, B. R.; Strottman, D.
1998-01-01
Various models for pion multiplicity distributions produced in relativistic heavy ion collisions are discussed. The models include a relativistic hydrodynamic model, a thermodynamic description, an emitting source pion laser model, and a description which generates a negative binomial description. The approach developed can be used to discuss other cases which will be mentioned. The pion probability distributions for these various cases are compared. Comparison of the pion laser model and Bos...
Thelwall, Mike
2016-01-01
Identifying the statistical distribution that best fits citation data is important to allow robust and powerful quantitative analyses. Whilst previous studies have suggested that both the hooked power law and discretised lognormal distributions fit better than the power law and negative binomial distributions, no comparisons so far have covered all articles within a discipline, including those that are uncited. Based on an analysis of 26 different Scopus subject areas in seven different years...
Probabilistic Inspection of Multimodally Distributed Signals
Czech Academy of Sciences Publication Activity Database
Ettler, P.; Puchr, I.; Jirsa, Ladislav; Pavelková, Lenka
Oxford, UK: The British Institute of Non-Destructive Testing, 2015. ISBN 978-1-5108-0712-9. [The 12th International Conference on Condition Monitoring and Machinery Failure Prevention Technologies (CM 2015/MFPT 2015). Oxford (GB), 09.06.2015-11.06.2015] R&D Projects: GA MŠk 7D12004 Institutional support: RVO:67985556 Keywords : condition monitoring * probabilistic logic * binomial opinion * multimodally distributed signal * Gaussian mixture Subject RIV: BC - Control Systems Theory http://library.utia.cas.cz/separaty/2015/AS/jirsa-0444754.pdf
Gastón Silverio Milanesi
2013-01-01
El trabajo propone un modelo de valoración de opciones reales con base en el modelo binomial utilizando la transformación de Edgeworth (Rubinstein, 1998) para incorporar momentos estocásticos de orden superior, especialmente para ciertos tipos de organizaciones, como empresas de base tecnológica, donde no se dispone de cartera de activos financieros gemelos, comparables de mercado y procesos estocásticos no gaussianos. Primero, se presenta el desarrollo formal del modelo, luego su aplicación ...
Hadronic overlap and total multiplicity distributions in high energy physics collisions
International Nuclear Information System (INIS)
In the realm of Chou and Yang's geometrical description of hadron collisions at high energy, the total multiplicity distribution of negative binomial type for non-leading secondaries is compounded from a Poisson and a gamma distribution. The latter is attributed to overlap in space-time of the colliding hadrons. The overlap is defined here in terms of local interaction probabilities for each incident hadron. These probabilities are assumed to be similar but not identical to hadron constituent quark densities. They are predicted to approach the densities for growing energy. This as well as the resulting integrated overlap are borne out by the empirical data on the negative binomial distribution in an unambiguous way. The preponderance of the latter at very high energies thus reflects non-relativistic spatial hadron structure and incoherence of event-like excitations throughout the overlap region. 9 refs.; 6 figs
Distribution of odds ratio in 2 × 2 contingency table: adjustment for correlation.
Biswas, Atanu; Hwang, Jing-Shiang
2011-01-01
The Log-odds ratio for 2 × 2 contingency tables is often approximated by a normal distribution with an approximated variance. Hwang and Biswas (2008) illustrated that the standard expression for the variance should be modified in the presence of correlation. They also provided an adjustment to this variance expression when a single 2 × 2 table is available with matched-pair data. In this present paper, we first provide the required adjustment for multiple 2 × 2 tables, theoretically and also with reference to some data examples. We illustrate that this variance-adjusted normal approximation is a better approximation for such data. We provide two examples, one of which came from a late-phase clinical trial. As the theoretical development of this research depends on the existence of a bivariate binomial distribution, a multivariate (and hence bivariate) binomial distribution is motivated and derived. We then provide a suitably correlation adjusted Mantel-Haenszel test procedure. PMID:21191860
Node degree distribution in spanning trees
International Nuclear Information System (INIS)
A method is presented for computing the number of spanning trees involving one link or a specified group of links, and excluding another link or a specified group of links, in a network described by a simple graph in terms of derivatives of the spanning-tree generating function defined with respect to the eigenvalues of the Kirchhoff (weighted Laplacian) matrix. The method is applied to deduce the node degree distribution in a complete or randomized set of spanning trees of an arbitrary network. An important feature of the proposed method is that the explicit construction of spanning trees is not required. It is shown that the node degree distribution in the spanning trees of the complete network is described by the binomial distribution. Numerical results are presented for the node degree distribution in square, triangular, and honeycomb lattices. (paper)
Ghosh, Dipak; Deb, Argha; Lahiri, Madhumita Banerjee; Mandal, Pasupati; Biswas, Subrata; Ghosh, Jayita; Bhattacharyya, Swarnapratim; Haldar, Prabir Kumar; Maity, Dipak
This work presents a study on the multiplicity distribution of shower and compound multiplicity (pions + target protons) emitted from 12C-AgBr and 24Mg-AgBr interactions at 4.5 AGeV in terms of negative binomial distribution (NBD) and also on the fluctuation pattern of shower and compound multiplicity in the frame work of two-dimensional factorial moment methodology using the concept of Hurst exponent.
Theorem of Decomposition for Random Variable of Negative Binomial Distribution%负二项分布随机变量的分解定理
Institute of Scientific and Technical Information of China (English)
熊加兵; 陈光曙
2008-01-01
给出了负二项分布的分解定理,并进一步研究了负二项分布的有关性质和近似计算公式.在复杂排队系统中离散状态下顾客等待时间分布的概率计算中起到了重要作用.
Institute of Scientific and Technical Information of China (English)
陈卓恒
2011-01-01
讨论一类散度偏大的分布负二项分布的相关性质,以服从负二项分布的索赔次数为响应变量,引入风险分级变量和对数联结函数,建立广义线性模型.采用极大似然估计法进行参数估计,并用Wald检验法进行检验.最后,利用SAS软件包对一组保险索赔数据进行实证分析.
Empirical Bayesian estimation for negative binomial distribution reliability%负二项分布可靠度的经验Bayes估计
Institute of Scientific and Technical Information of China (English)
纪志荣
2009-01-01
在平方损失函数下,获得了负二项分布可靠度θ的Bayes估计,在一般条件下,利用其边缘分布的特性,构造了相应的经验Bayes估计,并证明了得到的EB估计是相合的渐近最优的.
Analysis of the negative binomial distribution and test of population pattern%负二项式分布及种群格局检验分析
Institute of Scientific and Technical Information of China (English)
马钦彦
2009-01-01
种群格局是种群生态学的重要研究内容之一.该文介绍了随机、均匀和集群3类种群空间格局的基本类型,以及与其相对应的概率分布函数,如正二项式分布、泊松分布和集群分布,重点讨论了在种群格局研究中被广泛应用的负二项式分布的内涵、分布函数的建立和参数的估计,对种群格局检验常用指标及其使用中存在的错误也进行了分析和讨论.
Empirical Bayes Estimation for the Negative Binomial Distribution Reliability%负二项分布可靠度的经验Bayes估计
Institute of Scientific and Technical Information of China (English)
唐军民; 王成名
2005-01-01
本文在平方损失下,给出了负二项分布可靠度θ的Bayes估计、Bayes置信下限,同时构造了θ的渐近最优的经验Bayes(EB)估计,并证明了该EB估计的收敛速度为O(n-1).
A study on structures of two kind negative binomial distributions%负二项分布的结构研究
Institute of Scientific and Technical Information of China (English)
康殿统
2015-01-01
给出了负二项分布的两个不同定义与一个结构性定理.研究了两类负二项随机变量的无穷可分性.给出了求两类负二项随机变量的期望、方差与矩母函数的几种简捷方法.另外给出了涉及负二项随机变量的两个计算实例.
Tannenbaum, M. J.
1994-01-01
The concept of "Intermittency" was introduced by Bialas and Peschanski to try to explain the "large" fluctuations of multiplicity in restricted intervals of rapidity or pseudorapidity. A formalism was proposed to to study non-statistical (more precisely, non-Poisson) fluctuations as a function of the size of rapidity interval, and it was further suggested that the "spikes" in the rapidity fluctuations were evidence of fractal or intermittent behavior, in analogy to turbulence in fluid dynamics which is characterized by self-similar fluctuations at all scales-the absence of well defined scale of length.
E-Bayesian Estimation of the Negative Binomial Distribution Reliability%负二项分布可靠度的E-Bayes估计
Institute of Scientific and Technical Information of China (English)
苏清华; 胡中波
2011-01-01
对负二项分布,给出在熵损失函数下当可靠度的先验分布为Beta分布和幂分布时可靠度的Bayes估计、E-Bayes估计及多层Bayes估计,并针对先验分布为幂分布的情形设计了相应的数值实验.实验结果表明,相对于负二项分布可靠度的多层Bayes估计,其E-Bayes估计的计算更简单,且稳健性也更好.
Institute of Scientific and Technical Information of China (English)
牛燕影; 王增富; 田乃硕
2005-01-01
在研究只允许部分服务台进入休假状态的多服务台M/M/c排队系统时,我们发现了条件Erlang分布的一些有趣的性质,进一步研究我们发现相对应离散随机状态的负二项分布也具有很好的性质(概率封闭性).本文证明了一类负二项分布的概率封闭性.它们对导出复杂排队系统中离散状态下顾客等待时间分布及保险公司中破产概率上界的计算起着重要作用.
Institute of Scientific and Technical Information of China (English)
徐伟; 矫思琦; 张玲; 高扬; 陈孝国
2014-01-01
针对负二项分布的参数采用Bayes方法进行估计.首先,讨论了平方损失函数下负二项分布参数的估计问题,尤其是建立了新的平衡损失函数,获得了负二项分布参数的无偏估计.其次,讨论了负二项分布与Poisson分布之间的关系.最后给出了熵损失函数下负二项分布参数的估计.
Information of Structures in Galaxy Distribution
Fang, Fan
2006-06-01
We introduce an information-theoretic measure, the Rényi information, to describe the galaxy distribution in space. We discuss properties of the information measure and demonstrate its relationship with the probability distribution function and multifractal descriptions. Using the First Look Survey galaxy samples observed by the Infrared Array Camera on board the Spitzer Space Telescope, we present measurements of the Rényi information, as well as the counts-in-cells distribution and multifractal properties of galaxies in mid-infrared wavelengths. Guided by a multiplicative cascade simulation based on a binomial model, we verify our measurements and discuss the spatial selection effects on measuring information of the spatial structures. We derive structure scan functions at scales where selection effects are small for the Spitzer samples. We discuss the results and the potential of applying the Rényi information to the measurement of other spatial structures.
Information of Structures in Galaxy Distribution
Fang, F
2006-01-01
We introduce an information-theoretic measure, the Renyi information, to describe the galaxy distribution in space. We discuss properties of the information measure, and demonstrate its relationship with the probability distribution function and multifractal descriptions. Using the First Look Survey galaxy samples observed by the Infrared Array Camera onboard Spitzer Space Telescope, we present measurements of the Renyi information, as well as the counts-in-cells distribution and multifractal properties of galaxies in mid-infrared wavelengths. Guided by multiplicative cascade simulation based on a binomial model, we verify our measurements, and discuss the spatial selection effects on measuring information of the spatial structures. We derive structure scan functions at scales where selection effects are small for the Spitzer samples. We discuss the results, and the potential of applying the Renyi information to measuring other spatial structures.
Forms and genesis of species abundance distributions
Directory of Open Access Journals (Sweden)
Evans O. Ochiaga
2015-12-01
Full Text Available Species abundance distribution (SAD is one of the most important metrics in community ecology. SAD curves take a hollow or hyperbolic shape in a histogram plot with many rare species and only a few common species. In general, the shape of SAD is largely log-normally distributed, although the mechanism behind this particular SAD shape still remains elusive. Here, we aim to review four major parametric forms of SAD and three contending mechanisms that could potentially explain this highly skewed form of SAD. The parametric forms reviewed here include log series, negative binomial, lognormal and geometric distributions. The mechanisms reviewed here include the maximum entropy theory of ecology, neutral theory and the theory of proportionate effect.
Tsagris, Michael; Elmatzoglou, Ioannis; Christos C. Frangos
2015-01-01
Little attention has been given to the correlation coefficient when data come from discrete or continuous non-normal populations. In this article, we consider the efficiency of two correlation coefficients which are from the same family, Pearson's and Spearman's estimators. Two discrete bivariate distributions were examined: the Poisson and the Negative Binomial. The comparison between these two estimators took place using classical and bootstrap techniques for the construction of confidence ...
Tsagris, Michail; Elmatzoglou, Ioannis; C. Frangos, Christos
2012-01-01
Little attention has been given to the correlation coefficient when data come from discrete or continuous non-normal populations. In this article, we consider the efficiency of two correlation coefficients which are from the same family, Pearson's and Spearman's estimators. Two discrete bivariate distributions were examined: the Poisson and the Negative Binomial. The comparison between these two estimators took place using classical and bootstrap techniques for the construction of confidence ...
Dividend Decision under Distributed Profit Taxation: Investorís Perspective
Aaro Hazak
2006-01-01
Distributed profit taxation is the corporate taxation regime of Estonia. A theoretical model on dividend policy under this tax system, compared to traditional gross profit taxation, is presented in this paper. The paper seeks to model a company operating under uncertainty in a binomial framework, including company and investor level taxes and investorís different consumption levels. Overall, the tax effects on different forms of payout (e.g. dividends or share repurchases) are equal under thi...
High--Energy Multiparticle Distributions and a Generalized Lattice Gas Model
Jackson, A D; Wettig, T.; Balazs, N. L.
1993-01-01
A simple lattice gas model in one dimension is constructed in which each site can be occupied by at most one particle of any one of $D$ species. Particles interact with a randomly drawn nearest neighbor interaction. This model is capable of reproducing the factorial moments observed in high--energy scattering. In the limit $D \\rightarrow \\infty$, the factorial moments of the negative binomial distribution are obtained naturally.
Measurements of the charged particle multiplicity distribution in restricted rapidity intervals
Buskulic, Damir; De Bonis, I; Décamp, D; Ghez, P; Goy, C; Lees, J P; Lucotte, A; Minard, M N; Odier, P; Pietrzyk, B; Ariztizabal, F; Chmeissani, M; Crespo, J M; Efthymiopoulos, I; Fernández, E; Fernández-Bosman, M; Gaitan, V; Garrido, L; Martínez, M; Orteu, S; Pacheco, A; Padilla, C; Palla, Fabrizio; Pascual, A; Perlas, J A; Sánchez, F; Teubert, F; Colaleo, A; Creanza, D; De Palma, M; Farilla, A; Gelao, G; Girone, M; Iaselli, Giuseppe; Maggi, G; Maggi, M; Marinelli, N; Natali, S; Nuzzo, S; Ranieri, A; Raso, G; Romano, F; Ruggieri, F; Selvaggi, G; Silvestris, L; Tempesta, P; Zito, G; Huang, X; Lin, J; Ouyang, Q; Wang, T; Xie, Y; Xu, R; Xue, S; Zhang, J; Zhang, L; Zhao, W; Bonvicini, G; Cattaneo, M; Comas, P; Coyle, P; Drevermann, H; Engelhardt, A; Forty, Roger W; Frank, M; Hagelberg, R; Harvey, J; Jacobsen, R; Janot, P; Jost, B; Knobloch, J; Lehraus, Ivan; Markou, C; Martin, E B; Mato, P; Meinhard, H; Minten, Adolf G; Miquel, R; Oest, T; Palazzi, P; Pater, J R; Pusztaszeri, J F; Ranjard, F; Rensing, P E; Rolandi, Luigi; Schlatter, W D; Schmelling, M; Schneider, O; Tejessy, W; Tomalin, I R; Venturi, A; Wachsmuth, H W; Wiedenmann, W; Wildish, T; Witzeling, W; Wotschack, J; Ajaltouni, Ziad J; Bardadin-Otwinowska, Maria; Barrès, A; Boyer, C; Falvard, A; Gay, P; Guicheney, C; Henrard, P; Jousset, J; Michel, B; Monteil, S; Montret, J C; Pallin, D; Perret, P; Podlyski, F; Proriol, J; Rossignol, J M; Saadi, F; Fearnley, Tom; Hansen, J B; Hansen, J D; Hansen, J R; Hansen, P H; Nilsson, B S; Kyriakis, A; Simopoulou, Errietta; Siotis, I; Vayaki, Anna; Zachariadou, K; Blondel, A; Bonneaud, G R; Brient, J C; Bourdon, P; Passalacqua, L; Rougé, A; Rumpf, M; Tanaka, R; Valassi, Andrea; Verderi, M; Videau, H L; Candlin, D J; Parsons, M I; Focardi, E; Parrini, G; Corden, M; Delfino, M C; Georgiopoulos, C H; Jaffe, D E; Antonelli, A; Bencivenni, G; Bologna, G; Bossi, F; Campana, P; Capon, G; Chiarella, V; Felici, G; Laurelli, P; Mannocchi, G; Murtas, F; Murtas, G P; Pepé-Altarelli, M; Dorris, S J; Halley, A W; ten Have, I; Knowles, I G; Lynch, J G; Morton, W T; O'Shea, V; Raine, C; Reeves, P; Scarr, J M; Smith, K; Smith, M G; Thompson, A S; Thomson, F; Thorn, S; Turnbull, R M; Becker, U; Braun, O; Geweniger, C; Graefe, G; Hanke, P; Hepp, V; Kluge, E E; Putzer, A; Rensch, B; Schmidt, M; Sommer, J; Stenzel, H; Tittel, K; Werner, S; Wunsch, M; Beuselinck, R; Binnie, David M; Cameron, W; Colling, D J; Dornan, Peter J; Konstantinidis, N P; Moneta, L; Moutoussi, A; Nash, J; San Martin, G; Sedgbeer, J K; Stacey, A M; Dissertori, G; Girtler, P; Kneringer, E; Kuhn, D; Rudolph, G; Bowdery, C K; Brodbeck, T J; Colrain, P; Crawford, G; Finch, A J; Foster, F; Hughes, G; Sloan, Terence; Whelan, E P; Williams, M I; Galla, A; Greene, A M; Kleinknecht, K; Quast, G; Raab, J; Renk, B; Sander, H G; Wanke, R; Zeitnitz, C; Aubert, Jean-Jacques; Bencheikh, A M; Benchouk, C; Bonissent, A; Bujosa, G; Calvet, D; Carr, J; Diaconu, C A; Etienne, F; Thulasidas, M; Nicod, D; Payre, P; Rousseau, D; Talby, M; Abt, I; Assmann, R W; Bauer, C; Blum, Walter; Brown, D; Dietl, H; Dydak, Friedrich; Ganis, G; Gotzhein, C; Jakobs, K; Kroha, H; Lütjens, G; Lutz, Gerhard; Männer, W; Moser, H G; Richter, R H; Rosado-Schlosser, A; Settles, Ronald; Seywerd, H C J; Stierlin, U; Saint-Denis, R; Wolf, G; Alemany, R; Boucrot, J; Callot, O; Cordier, A; Courault, F; Davier, M; Duflot, L; Grivaz, J F; Jacquet, M; Kim, D W; Le Diberder, F R; Lefrançois, J; Lutz, A M; Musolino, G; Nikolic, I A; Park, H J; Park, I C; Schune, M H; Simion, S; Veillet, J J; Videau, I; Abbaneo, D; Azzurri, P; Bagliesi, G; Batignani, G; Bettarini, S; Bozzi, C; Calderini, G; Carpinelli, M; Ciocci, M A; Ciulli, V; Dell'Orso, R; Fantechi, R; Ferrante, I; Foà, L; Forti, F; Giassi, A; Giorgi, M A; Gregorio, A; Ligabue, F; Lusiani, A; Marrocchesi, P S; Messineo, A; Rizzo, G; Sanguinetti, G; Sciabà, A; Spagnolo, P; Steinberger, Jack; Tenchini, Roberto; Tonelli, G; Triggiani, G; Vannini, C; Verdini, P G; Walsh, J; Betteridge, A P; Blair, G A; Bryant, L M; Cerutti, F; Gao, Y; Green, M G; Johnson, D L; Medcalf, T; Mir, M; Perrodo, P; Strong, J A; Bertin, V; Botterill, David R; Clifft, R W; Edgecock, T R; Haywood, S; Edwards, M; Maley, P; Norton, P R; Thompson, J C; Bloch-Devaux, B; Colas, P; Duarte, H; Emery, S; Kozanecki, Witold; Lançon, E; Lemaire, M C; Locci, E; Marx, B; Pérez, P; Rander, J; Renardy, J F; Rosowsky, A; Roussarie, A; Schuller, J P; Schwindling, J; Si Mohand, D; Trabelsi, A; Vallage, B; Johnson, R P; Kim, H Y; Litke, A M; McNeil, M A; Taylor, G; Beddall, A; Booth, C N; Boswell, R; Cartwright, S L; Combley, F; Dawson, I; Köksal, A; Letho, M; Newton, W M; Rankin, C; Thompson, L F; Böhrer, A; Brandt, S; Cowan, G D; Feigl, E; Grupen, Claus; Lutters, G; Minguet-Rodríguez, J A; Rivera, F; Saraiva, P; Smolik, L; Stephan, F; Apollonio, M; Bosisio, L; Della Marina, R; Giannini, G; Gobbo, B; Ragusa, F; Rothberg, J E; Wasserbaech, S R; Armstrong, S R; Bellantoni, L; Elmer, P; Feng, Z; Ferguson, D P S; Gao, Y S; González, S; Grahl, J; Harton, J L; Hayes, O J; Hu, H; McNamara, P A; Nachtman, J M; Orejudos, W; Pan, Y B; Saadi, Y; Schmitt, M; Scott, I J; Sharma, V; Turk, J; Walsh, A M; Wu Sau Lan; Wu, X; Yamartino, J M; Zheng, M; Zobernig, G
1995-01-01
Charged particle multiplicity distributions have been measured with the ALEPH detector in restricted rapidity intervals |Y| \\leq 0.5,1.0, 1.5,2.0\\/ along the thrust axis and also without restriction on rapidity. The distribution for the full range can be parametrized by a log-normal distribution. For smaller windows one finds a more complicated structure, which is understood to arise from perturbative effects. The negative-binomial distribution fails to describe the data both with and without the restriction on rapidity. The JETSET model is found to describe all aspects of the data while the width predicted by HERWIG is in significant disagreement.
Directory of Open Access Journals (Sweden)
Gastón Silverio Milanesi
2014-06-01
Full Text Available En este documento se propone un modelo binomial para valorar empresas, proyectando y condicionando escenarios de continuidad o liquidación de la firma. El modelo se basa en la Teoría de Opciones Reales para estimar el valor de la firma, que resulta de un balance explícito de las ventajas y riesgos de tomar deuda. El trabajo se estructura de la siguiente manera: Primeramente, la introducción y desarrollo del modelo teórico; luego se ilustra mediante un caso de aplicación, comparando los resultados obtenidos con el modelo de descuento de flujos de fondos. Se sensibilizan variables como: endeudamiento, tasa de impuesto y volatilidad para analizar el impacto en el valor de la empresa. Finalmente, se describen las ventajas del modelo propuesto.
Statistical Distributions of Earthquake Numbers: Consequence of Branching Process
Kagan, Yan Y
2009-01-01
We discuss various statistical distributions of earthquake numbers. Previously we derived several discrete distributions to describe earthquake numbers for the branching model of earthquake occurrence: these distributions are the Poisson, geometric, logarithmic, and the negative binomial (NBD). In particular, a point branching process along the magnitude (or log seismic moment) axis with independent events (immigrants) explains the magnitude/moment-frequency relation and the NBD of earthquake counts in large time/space windows, as well as the dependence of the NBD parameters on the magnitude threshold. We discuss applying these distributions, especially the NBD, to approximate event numbers in earthquake catalogs. There are many different representations of the NBD. Most can be traced either to the Pascal distribution or to the mixture of the Poisson distribution with the gamma law. We discuss advantages and drawbacks of both representations for statistical analysis of earthquake catalogs. We also consider ap...
The Degree Distribution of the Random Multigraphs
Institute of Scientific and Technical Information of China (English)
Ai Lian CHEN; Fu Ji ZHANG; Hao LI
2012-01-01
In this paper,as a generalization of the binomial random graph model,we define the model of multigraphs as follows:let (Q)(n; {pk}) be the probability space of all the labelled loopless multigraphs with vertex set V ={v1,v2,...,vn },in which the distribution of tvi,vj,the number of the edges between any two vertices vi and vj isP{tvi,vj =k} =pk, k =0,1,2,...and they are independent of each other.Denote by Xd =Xd(G),Yd =Yd(G),Zd =Zd(G) and Zcd =Zed(G) the number of vertices of G with degree d,at least d,at most d and between c and d.In this paper,we discuss the distribution of Xd,Yd,Zd and Zcd in the probability space (Q)(n; {pk}).
Finding a minimally informative Dirichlet prior distribution using least squares
International Nuclear Information System (INIS)
In a Bayesian framework, the Dirichlet distribution is the conjugate distribution to the multinomial likelihood function, and so the analyst is required to develop a Dirichlet prior that incorporates available information. However, as it is a multiparameter distribution, choosing the Dirichlet parameters is less straightforward than choosing a prior distribution for a single parameter, such as p in the binomial distribution. In particular, one may wish to incorporate limited information into the prior, resulting in a minimally informative prior distribution that is responsive to updates with sparse data. In the case of binomial p or Poisson λ, the principle of maximum entropy can be employed to obtain a so-called constrained noninformative prior. However, even in the case of p, such a distribution cannot be written down in the form of a standard distribution (e.g., beta, gamma), and so a beta distribution is used as an approximation in the case of p. In the case of the multinomial model with parametric constraints, the approach of maximum entropy does not appear tractable. This paper presents an alternative approach, based on constrained minimization of a least-squares objective function, which leads to a minimally informative Dirichlet prior distribution. The alpha-factor model for common-cause failure, which is widely used in the United States, is the motivation for this approach, and is used to illustrate the method. In this approach to modeling common-cause failure, the alpha-factors, which are the parameters in the underlying multinomial model for common-cause failure, must be estimated from data that are often quite sparse, because common-cause failures tend to be rare, especially failures of more than two or three components, and so a prior distribution that is responsive to updates with sparse data is needed.
Finding the Right Distribution for Highly Skewed Zero-inflated Clinical Data
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Resmi Gupta
2013-03-01
Full Text Available Discrete, highly skewed distributions with excess numbers of zeros often result in biased estimates and misleading inferences if the zeros are not properly addressed. A clinical example of children with electrophysiologic disorders in which many of the children are treated without surgery is provided. The purpose of the current study was to identify the optimal modeling strategy for highly skewed, zeroinflated data often observed in the clinical setting by: (a simulating skewed, zero-inflated count data; (b fitting simulated data with Poisson, Negative Binomial, Zero-Inflated Poisson (ZIP and Zero-inflated Negative Binomial (ZINB models; and, (c applying the aforementioned models to actual, highlyskewed, clinical data of children with an EP disorder. The ZIP model was observed to be the optimal model based on traditional fit statistics as well as estimates of bias, mean-squared error, and coverage.
The galaxy counts-in-cells distribution from the SDSS
Yang, Abel
2010-01-01
We determine the galaxy counts-in-cells distribution from the Sloan Digital Sky Survey (SDSS) for 3D spherical cells in redshift space as well as for 2D projected cells. We find that cosmic variance in the SDSS causes the counts-in-cells distributions in different quadrants to differ from each other by up to 20%. We also find that within this cosmic variance, the overall galaxy counts-in-cells distribution agrees with both the gravitational quasi-equilibrium distribution and the negative binomial distribution. We also find that brighter galaxies are more strongly clustered than if they were randomly selected from a larger complete sample that includes galaxies of all luminosities. The results suggest that bright galaxies could be in dark matter haloes separated by less than ~10 Mpc/h.
K-distribution and polarimetric terrain radar clutter
Yueh, S. H.; Kong, J. A.; Jao, J. K.; Shin, R. T.; Novak, L. M.
1989-01-01
A multivariate K-distribution is proposed to model the statistics of fully polarimetric radar data from earth terrain with polarizations HH, HV, VH, and VV. In this approach, correlated polarizations of radar signals, as characterized by a covariance matrix, are treated as the sum of N n-dimensional random vectors; N obeys the negative binomial distribution with a parameter alpha and mean N-bar. Subsequently, an n-dimensional K-distribution, with either zero or nonzero mean, is developed in the limit of infinite N-bar or illuminated area. The probability density function (PDF) of the K-distributed vector normalized by its Euclidean norm is independent of the parameter alpha and is the same as that derived from a zero-mean Gaussian-distributed random vector.
Institute of Scientific and Technical Information of China (English)
吴祝慧
2008-01-01
在Bayes分析中,先验分布的选取是其基本问题,尤其是在无先验信息的情况下,如何确定先验分布更是Bayes学派关注的焦点.基于Jeffreys提出的利用Fisher信息矩阵确定无信息先验分布的方法,给出了负二项分布和Weibull分布的先验分布公式.
Adejumo, A. O.; Heumann, Christian; Toutenburg, Helge
2004-01-01
The Poisson distribution has been widely used for modelling rater agreement using loglinear models. Mostly in all life or social science researches, subjects are being classified into categories by rater, interviewers or observers and most of these tables indicate that the cell counts are mixtures of either too big values and two small values or zeroes which are sparse data. We refer to sparse as a situation when a large number of cell frequencies are very small. For these kinds of tables, th...
Measurement of xenon distribution statistics in Na-A zeolite cavities
International Nuclear Information System (INIS)
129Xe NMR spectroscopy has been used to probe directly the distribution of xenon atoms confined in atomic-size Na-A zeolite cavities. For mean xenon occupancies less than about three Xe atoms per α-cage, the guest populations are well described by binomial statistics. At higher guest loadings the finite volumes of the xenon atoms become significant, as reflected by a fit of the experimental populations with a hypergeometric distribution. The data and hypergeometric analysis indicate a maximum occupancy of seven Xe atoms/cage. At the highest xenon loadings the experimental distribution is narrower than hypergeometric
Finding a Minimally Informative Dirichlet Prior Distribution Using Least Squares
International Nuclear Information System (INIS)
In a Bayesian framework, the Dirichlet distribution is the conjugate distribution to the multinomial likelihood function, and so the analyst is required to develop a Dirichlet prior that incorporates available information. However, as it is a multiparameter distribution, choosing the Dirichlet parameters is less straight-forward than choosing a prior distribution for a single parameter, such as p in the binomial distribution. In particular, one may wish to incorporate limited information into the prior, resulting in a minimally informative prior distribution that is responsive to updates with sparse data. In the case of binomial p or Poisson, the principle of maximum entropy can be employed to obtain a so-called constrained noninformative prior. However, even in the case of p, such a distribution cannot be written down in closed form, and so an approximate beta distribution is used in the case of p. In the case of the multinomial model with parametric constraints, the approach of maximum entropy does not appear tractable. This paper presents an alternative approach, based on constrained minimization of a least-squares objective function, which leads to a minimally informative Dirichlet prior distribution. The alpha-factor model for common-cause failure, which is widely used in the United States, is the motivation for this approach, and is used to illustrate the method. In this approach to modeling common-cause failure, the alpha-factors, which are the parameters in the underlying multinomial aleatory model for common-cause failure, must be estimated from data that is often quite sparse, because common-cause failures tend to be rare, especially failures of more than two or three components, and so a prior distribution that is responsive to updates with sparse data is needed.
Ghosh, Premomoy; Muhuri, Sanjib
2014-01-01
Measured multiplicity distributions of primary charged particles produced in the forward rapidity region of the $proton-proton$ ($pp$) collisions at the centre-of-mass energy, $\\sqrt {s}$ = 7 TeV at the Large Hadron Collider (LHC) have been analyzed in terms of the Negative Binomial Distribution (NBD) function. Like the multiplicity distributions in the mid-rapidity region for the $pp$ collisions at $\\sqrt {s}$ = 7 TeV, the distributions for the minimum bias events in the forward region also ...
Multiplicity distribution of particles produced in 3.7 A GeV/c 16O-AgBr collisions
International Nuclear Information System (INIS)
Multiplicity distribution of secondary particles is regarded a very sensitive characteristics of relativistic nuclear collisions for testing predictions of various phenomenological and theoretical models proposed to explain the mechanism of multiparticle production in such collisions. From the study of multiplicity distributions of relativistic charged particles, ns and compound multiplicity, nc of the particles produced in 3.7 A GeV/c 16O-AgBr collisions, it is concluded that both the distributions can be nicely reproduced by negative binomial distribution (NBD) and this observation is also supported by the Monte Carlo AMPT model
Discrete stochastic metapopulation model with arbitrarily distributed infectious period.
Hernandez-Ceron, Nancy; Chavez-Casillas, Jonathan A; Feng, Zhilan
2015-03-01
In this study, a stochastic discrete-time model is developed to study the spread of an infectious disease in an n-patch environment. The model includes an arbitrary distribution of the (random) infectious period T, and the results are used to investigate how the distribution of T may influence the model outcomes. General results are applied to specific distributions including Geometric, Negative Binomial, Poisson and Uniform. The model outcomes are contrasted both numerically and analytically by comparing the corresponding basic reproduction numbers R0 and probability of a minor epidemic (or probability of disease extinction) P0. It is shown analytically that for n = 2 the reproduction numbers corresponding to different distributions of T can be ordered based on the probability generating function ϕT of T. In addition, numerical simulations are carried out to examine the final epidemic size F and duration of the epidemic D of a two-patch model. PMID:25550286
How to retrieve additional information from the multiplicity distributions
Wilka, Grzegorz
2016-01-01
Multiplicity distributions $P(N)$ measured in multiparticle production processes are most frequently described by the Negative Binomial Distribution (NBD). However, with increasing collision energy some systematic discrepancies become more and more apparent. They are usually attributed to the possible multi-source structure of the production process and described using a multi-NBD form of the multiplicity distribution. We investigate the possibility of keeping a single NBD but with its parameters depending on the multiplicity $N$. This is done by modifying the widely known clan model of particle production leading to the NBD form of $P(N)$. This is then confronted with the approach based on the so-called cascade-stochastic formalism which is based on different types of recurrence relations defining $P(N)$. We demonstrate that a combination of both approaches allows the retrieval of additional valuable information from the multiplicity distributions, namely the oscillatory behavior of the counting statistics a...
Directory of Open Access Journals (Sweden)
Gastón Silverio Milanesi
2014-01-01
Full Text Available El trabajo tiene por objeto exponer la metodología, las ventajas y las debilidades del modelo binomial borroso de valoración de opciones reales como complemento del modelo binomial probabilístico. Para lograr lo anterior primero se presentan los modelos de opciones reales clasificados en probabilístico y borroso; luego se desarrolla el modelo binomial borroso incorporando: el método Marketed Asset Disclai- mer (MAD, rejillas binomiales borrosas y el índice pesimismo-optimismo, para estimar el valor esperado de las opciones del proyecto (VEOP. Se ilustra con un caso comparando los resultados obtenidos con el modelo borroso y el probabilístico. Finalmente se concluye que, en situaciones de falta de información (ambigüedad, la lógica borrosa es un complemento del modelo probabilístico para determinar el valor de la flexibilidad estratégica. © 2012 Universidad ICESI. Publicado por Elsevier España, S.L. Todos los derechos reservados.
International Nuclear Information System (INIS)
Particle yields and fluctuations are studied in a general framework based on a cycle class picture in a Feynman path integral approach. Various cases such as the disoriented chiral condensate distribution, a negative binomial distribution, partially coherent state emission, and field emission from Lorentzian line shapes are discussed. Generalizations based on these important specific cases are developed. Connections of the cycle class picture with other approaches based on combinants, cumulants, hierarchical models, and clan variables are presented for the specific and general cases. A relation to a Feynman-Wilson gas and to the Ginzburg-Landau model are discussed
Mekjian, A. Z.
2002-01-01
Particle yields and fluctuations are studied in a general framework based on a cycle class picture in a Feynman path integral approach. Various cases such as the disoriented chiral condensate distribution, a negative binomial distribution, partially coherent state emission, and field emission from Lorentzian line shapes are discussed. Generalizations based on these important specific cases are developed. Connections of the cycle class picture with other approaches based on combinants, cumulants, hierarchical models, and clan variables are presented for the specific and general cases. A relation to a Feynman-Wilson gas and to the Ginzburg-Landau model are discussed.
Comparing distribution models for small samples of overdispersed counts of freshwater fish
Vaudor, Lise; Lamouroux, Nicolas; Olivier, Jean-Michel
2011-05-01
The study of species abundance often relies on repeated abundance counts whose number is limited by logistic or financial constraints. The distribution of abundance counts is generally right-skewed (i.e. with many zeros and few high values) and needs to be modelled for statistical inference. We used an extensive dataset involving about 100,000 fish individuals of 12 freshwater fish species collected in electrofishing points (7 m 2) during 350 field surveys made in 25 stream sites, in order to compare the performance and the generality of four distribution models of counts (Poisson, negative binomial and their zero-inflated counterparts). The negative binomial distribution was the best model (Bayesian Information Criterion) for 58% of the samples (species-survey combinations) and was suitable for a variety of life histories, habitat, and sample characteristics. The performance of the models was closely related to samples' statistics such as total abundance and variance. Finally, we illustrated the consequences of a distribution assumption by calculating confidence intervals around the mean abundance, either based on the most suitable distribution assumption or on an asymptotical, distribution-free (Student's) method. Student's method generally corresponded to narrower confidence intervals, especially when there were few (≤3) non-null counts in the samples.
Garrido-Balsells, José María; Jurado-Navas, Antonio; Paris, José Francisco; Castillo-Vazquez, Miguel; Puerta-Notario, Antonio
2015-03-01
In this paper, a novel and deeper physical interpretation on the recently published Málaga or ℳ statistical distribution is provided. This distribution, which is having a wide acceptance by the scientific community, models the optical irradiance scintillation induced by the atmospheric turbulence. Here, the analytical expressions previously published are modified in order to express them by a mixture of the known Generalized-K and discrete Binomial and Negative Binomial distributions. In particular, the probability density function (pdf) of the ℳ model is now obtained as a linear combination of these Generalized-K pdf, in which the coefficients depend directly on the parameters of the ℳ distribution. In this way, the Málaga model can be physically interpreted as a superposition of different optical sub-channels each of them described by the corresponding Generalized-K fading model and weighted by the ℳ dependent coefficients. The expressions here proposed are simpler than the equations of the original ℳ model and are validated by means of numerical simulations by generating ℳ -distributed random sequences and their associated histogram. This novel interpretation of the Málaga statistical distribution provides a valuable tool for analyzing the performance of atmospheric optical channels for every turbulence condition. PMID:25836855
Implications of heterogeneous distributions of organisms on ballast water sampling.
Costa, Eliardo G; Lopes, Rubens M; Singer, Julio M
2015-02-15
Ballast water sampling is one of the problems still needing investigation in order to enforce the D-2 Regulation of the International Convention for the Control and Management of Ship Ballast Water and Sediments. Although statistical "representativeness" of the sample is an issue usually discussed in the literature, neither a definition nor a clear description of its implications are presented. In this context, we relate it to the heterogeneity of the distribution of organisms in ballast water and show how to specify compliance tests under different models based on the Poisson and negative binomial distributions. We provide algorithms to obtain minimum sample volumes required to satisfy fixed limits on the probabilities of Type I and II errors. We show that when the sample consists of a large number of aliquots, the Poisson model may be employed even under moderate heterogeneity of the distribution of the organisms in the ballast water tank. PMID:25510550
Institute of Scientific and Technical Information of China (English)
生志荣
2011-01-01
负二项分布是一个重要的离散型随机变量的分布,可以用泊松分布和正态分布作为其近似分布,通过对两种近似分布进行比较分析,结果表明:在参数q很小时,泊松近似的精度好于正态近似,而且在参数口很小时,即便r不是很大,用泊松分布也能获得负二项分布较好的近似;当参数q较大时,泊松近似效果不好,相比之下,正态近似的结果不错.
Institute of Scientific and Technical Information of China (English)
王丙参; 魏艳华; 石春燕
2011-01-01
为了在模拟索赔次数时更好的运用泊松分布与负二项分布,研究了二者的优良特性及相互关系,最后结合Sas软件进行实例分析,得到了负二项分布是伽玛分布对泊松分布的混合分布且是赔频率强度存在正传 染性的索赔分布,由于方差大于均值,因而更好的描述非同质风险.
二项式系数与 Fibo nacci 数立方的一个关系%A relation between binomial coefficients and cubes of Fibonacci numbers
Institute of Scientific and Technical Information of China (English)
杨海; 李博; 高晓梅
2015-01-01
对于适合n≥ i≥0的整数n和i，设 ni ＝n！i！（n－ i）！是二项式系数；对于非负整数l，设Fl是第 l个Fibonacci数，对于给定的非负整数k和正整数n ，设 f （k ，3，n）是数列 n i n i＝0和｛F3k＋i｝ni＝0的卷积，即 f （k ，3，n）＝ n0 F3k ＋ n1 F3k＋1＋⋯＋ nn F3k＋n 。证明了当 k ≥ n时，等式 f （k ，3，n）＝15（2n F3k＋2n －（－1）k＋n3 Fk－n ）成立，当k ＜ n时，等式 f （k ，3，n）＝15（2n F3k＋2n ＋3 Fn－k ）成立。%For any integers n and i with n≥ i ≥ 0 ,let ni =n!i!(n - i)!be a binomial coefficient . For any nonnegative integer l ,let Fl be the l‐th Fibonacci number .Further ,for any fixed non‐negative integer k and any fixed positive integer n ,let f (k ,3 ,n) denotes the convolution of se‐quence ni ni= 0 and{F3k+ i}ni= 0 ,namely , f (k ,3 ,n) = n0 F3k + n1 F3k+1 + ⋯ + nn F3k+ n .It is proved that f(k ,3 ,n)= 15 (2nF3k+2n -(-1)k+n3Fk-n)or f(k ,3 ,n)= 15 (2nF3k+2n+3Fn-k)accord‐ing to k ≥ n or not .
Directory of Open Access Journals (Sweden)
D Johan Kotze
Full Text Available Temporal variation in the detectability of a species can bias estimates of relative abundance if not handled correctly. For example, when effort varies in space and/or time it becomes necessary to take variation in detectability into account when data are analyzed. We demonstrate the importance of incorporating seasonality into the analysis of data with unequal sample sizes due to lost traps at a particular density of a species. A case study of count data was simulated using a spring-active carabid beetle. Traps were 'lost' randomly during high beetle activity in high abundance sites and during low beetle activity in low abundance sites. Five different models were fitted to datasets with different levels of loss. If sample sizes were unequal and a seasonality variable was not included in models that assumed the number of individuals was log-normally distributed, the models severely under- or overestimated the true effect size. Results did not improve when seasonality and number of trapping days were included in these models as offset terms, but only performed well when the response variable was specified as following a negative binomial distribution. Finally, if seasonal variation of a species is unknown, which is often the case, seasonality can be added as a free factor, resulting in well-performing negative binomial models. Based on these results we recommend (a add sampling effort (number of trapping days in our example to the models as an offset term, (b if precise information is available on seasonal variation in detectability of a study object, add seasonality to the models as an offset term; (c if information on seasonal variation in detectability is inadequate, add seasonality as a free factor; and (d specify the response variable of count data as following a negative binomial or over-dispersed Poisson distribution.
Dias de Deus, Jorge; Ferreiro, E. G.; Pajares, C.; Ugoccioni, R.
2004-11-01
It is experimentally observed that the width of the KNO multiplicity distribution-or the negative binomial parameter, 1 / k-for pp collisions, in the energy region 10 ≲√{ s} ≲ 1800 GeV, is an increasing function of the energy. We argue that in models with parton or string saturation such trend will necessary change: at some energy the distribution will start to become narrower. In the framework of percolating strings, we have estimated the change to occur at an energy of the order of 5-10 TeV.
Dias de Deus, J; Pajares, C; Ugoccioni, R
2004-01-01
It is experimentally observed that the width of the KNO multiplicity distribution --or the negative binomial parameter 1/k-- for pp collisions, in the energy region 10 to 1800 GeV, is an increasing function of the energy. We argue that in models with parton or string saturation such trend will necessary change: at some energy the distribution will start to become narrower. In the framework of percolating strings, we have estimated the change to occur at an energy of the order of 5--10 TeV.
Criticality of the net-baryon number probability distribution at finite density
Morita, Kenji; Redlich, Krzysztof
2014-01-01
We compute the probability distribution $P(N)$ of the net-baryon number at finite temperature and quark-chemical potential, $\\mu$, at a physical value of the pion mass in the quark-meson model within the functional renormalization group scheme. For $\\mu/T<1$, the model exhibits the chiral crossover transition which belongs to the universality class of the $O(4)$ spin system in three dimensions. We explore the influence of the chiral crossover transition on the properties of the net baryon number probability distribution, $P(N)$. By considering ratios of $P(N)$ to the Skellam function, with the same mean and variance, we unravel the characteristic features of the distribution that are related to $O(4)$ criticality at the chiral crossover transition. We explore the corresponding ratios for data obtained at RHIC by the STAR Collaboration and discuss their implications. We also examine $O(4)$ criticality in the context of binomial and negative-binomial distributions for the net proton number.
Criticality of the net-baryon number probability distribution at finite density
Directory of Open Access Journals (Sweden)
Kenji Morita
2015-02-01
Full Text Available We compute the probability distribution P(N of the net-baryon number at finite temperature and quark-chemical potential, μ, at a physical value of the pion mass in the quark-meson model within the functional renormalization group scheme. For μ/T<1, the model exhibits the chiral crossover transition which belongs to the universality class of the O(4 spin system in three dimensions. We explore the influence of the chiral crossover transition on the properties of the net baryon number probability distribution, P(N. By considering ratios of P(N to the Skellam function, with the same mean and variance, we unravel the characteristic features of the distribution that are related to O(4 criticality at the chiral crossover transition. We explore the corresponding ratios for data obtained at RHIC by the STAR Collaboration and discuss their implications. We also examine O(4 criticality in the context of binomial and negative-binomial distributions for the net proton number.
Football fever: goal distributions and non-Gaussian statistics
Bittner, E.; Nußbaumer, A.; Janke, W.; Weigel, M.
2009-02-01
Analyzing football score data with statistical techniques, we investigate how the not purely random, but highly co-operative nature of the game is reflected in averaged properties such as the probability distributions of scored goals for the home and away teams. As it turns out, especially the tails of the distributions are not well described by the Poissonian or binomial model resulting from the assumption of uncorrelated random events. Instead, a good effective description of the data is provided by less basic distributions such as the negative binomial one or the probability densities of extreme value statistics. To understand this behavior from a microscopical point of view, however, no waiting time problem or extremal process need be invoked. Instead, modifying the Bernoulli random process underlying the Poissonian model to include a simple component of self-affirmation seems to describe the data surprisingly well and allows to understand the observed deviation from Gaussian statistics. The phenomenological distributions used before can be understood as special cases within this framework. We analyzed historical football score data from many leagues in Europe as well as from international tournaments, including data from all past tournaments of the “FIFA World Cup” series, and found the proposed models to be applicable rather universally. In particular, here we analyze the results of the German women’s premier football league and consider the two separate German men’s premier leagues in the East and West during the cold war times as well as the unified league after 1990 to see how scoring in football and the component of self-affirmation depend on cultural and political circumstances.
On the multiplicity distribution in statistical model: (II) most central collisions
Xu, Hao-jie
2016-01-01
This work is a continuation of our effort [arXiv:1602.06378] to investigate the statistical expectations for cumulants of (net-conserved) charge distributions in relativistic heavy ion collisions, by using a simple but quantitatively more realistic geometric model, i.e. optical Glauber model. We suggest a new approach for centrality definition in studying of multiplicity fluctuations, which aim at eliminating the uncertainties between experimental measurements and theoretical calculations, as well as redoubling the statistics. We find that the statistical expectations of multiplicity distribution mimic the negative binomial distribution at non-central collisions, but tend to approach the Poisson one at most central collisions due to the "boundary effect" from distribution of volume. We conclude that the collisional geometry (distribution of volume and its fluctuations) play a crucial role in studying of event-by-event multiplicity fluctuations in relativistic heavy ion collisions.
The Galaxy Counts-in-cells Distribution from the Sloan Digital Sky Survey
Yang, Abel; Saslaw, William C.
2011-03-01
We determine the galaxy counts-in-cells distribution from the Sloan Digital Sky Survey (SDSS) for three-dimensional spherical cells in redshift space as well as for two-dimensional projected cells. We find that cosmic variance in the SDSS causes the counts-in-cells distributions in different quadrants to differ from each other by up to 20%. We also find that within this cosmic variance, the overall galaxy counts-in-cells distribution agrees with both the gravitational quasi-equilibrium distribution and the negative binomial distribution. We also find that brighter galaxies are more strongly clustered than if they were randomly selected from a larger complete sample that includes galaxies of all luminosities. The results suggest that bright galaxies could be in dark matter halos separated by less than ~10 h -1 Mpc.
Selecting a distributional assumption for modelling relative densities of benthic macroinvertebrates
Gray, B.R.
2005-01-01
The selection of a distributional assumption suitable for modelling macroinvertebrate density data is typically challenging. Macroinvertebrate data often exhibit substantially larger variances than expected under a standard count assumption, that of the Poisson distribution. Such overdispersion may derive from multiple sources, including heterogeneity of habitat (historically and spatially), differing life histories for organisms collected within a single collection in space and time, and autocorrelation. Taken to extreme, heterogeneity of habitat may be argued to explain the frequent large proportions of zero observations in macroinvertebrate data. Sampling locations may consist of habitats defined qualitatively as either suitable or unsuitable. The former category may yield random or stochastic zeroes and the latter structural zeroes. Heterogeneity among counts may be accommodated by treating the count mean itself as a random variable, while extra zeroes may be accommodated using zero-modified count assumptions, including zero-inflated and two-stage (or hurdle) approaches. These and linear assumptions (following log- and square root-transformations) were evaluated using 9 years of mayfly density data from a 52 km, ninth-order reach of the Upper Mississippi River (n = 959). The data exhibited substantial overdispersion relative to that expected under a Poisson assumption (i.e. variance:mean ratio = 23 ??? 1), and 43% of the sampling locations yielded zero mayflies. Based on the Akaike Information Criterion (AIC), count models were improved most by treating the count mean as a random variable (via a Poisson-gamma distributional assumption) and secondarily by zero modification (i.e. improvements in AIC values = 9184 units and 47-48 units, respectively). Zeroes were underestimated by the Poisson, log-transform and square root-transform models, slightly by the standard negative binomial model but not by the zero-modified models (61%, 24%, 32%, 7%, and 0%, respectively
Directory of Open Access Journals (Sweden)
Vinay Mahajan
2012-06-01
Full Text Available Under the assumption that the encoders’ observations are conditionally independent Markov chains given an unobserved time-invariant random variable, results on the structure of optimal real-time encoding and decoding functions are obtained. The problem with noiseless channels and perfect memory at the receiver is then considered. A new methodology to find the structure of optimal real-time encoders is employed. A sufficient statistic with a time-invariant domain is found for this problem. This methodology exploits the presence of common information between the encoders and the receiver when communication is over noiseless channels. In this paper we estimate the lower bond, upper bond and define the encoder. In the previous design approach they follow Markov Chain approach to estimating the upper bound and define the encoder. In this dissertation we follow poison distribution to finding the lower bound and upper bound. Poisson can be viewed as an approximation to the binomial distribution. The approximation is good enough to be useful even when the sample size (N is only moderately large (say N > 50 and the probability (p is only relatively small (p < .2 The advantage of the Poisson distribution, of course, is that if N is large you need only know p to determine the approximate distribution of events. With the binomial distribution you also need to know N.
The distribution of the pathogenic nematode Nematodirus battus in lambs is zero-inflated
DEFF Research Database (Denmark)
Denwood, Matthew; Stear, M J; Matthews, L;
2008-01-01
Carlo methods to estimate the parameters of the zero-inflated negative binomial distribution. The analysis of 3000 simulated data sets indicated that this method out-performed the maximum likelihood procedure. Application of this technique to faecal egg counts from lambs in a commercial upland flock......Understanding the frequency distribution of parasites and parasite stages among hosts is essential for efficient experimental design and statistical analysis, and is also required for the development of sustainable methods of controlling infection. Nematodirus battus is one of the most important...... organisms that infect sheep but the distribution of parasites among hosts is unknown. An initial analysis indicated a high frequency of animals without N. battus and with zero egg counts, suggesting the possibility of a zero-inflated distribution. We developed a Bayesian analysis using Markov chain Monte...
Ghosh, Premomoy; Muhuri, Sanjib
2013-05-01
Measured multiplicity distributions of primary charged particles produced in the forward rapidity region of the proton-proton (pp) collisions at the center-of-mass energy, s=7TeV, at the LHC have been analyzed in terms of the negative binomial distribution function. Like the multiplicity distributions in the midrapidity region for the pp collisions at s=7TeV, the distributions for the minimum bias events in the forward region are also better described with the superposition of two negative binomail distributions, as proposed by a two-component model of particle production from two processes, the soft and the hard. However, the multiplicity distribution for the “hard-QCD” events in a large pseudorapidity window does not oblige the two-component model.
Lee, S J
2002-01-01
Various phenomenological models of particle multiplicity distributions are discussed using a general form of the grand canonical partition function. These phenomenological models include a wide range of varied processes such as coherent emission or Poisson processes, chaotic emission resulting in a negative binomial distribution, combinations of coherent and chaotic processes called signal/noise distributions, and models based on field emission from Lorentzian line shapes leading to Lorentz/Catalan distributions. These specific cases can be written as special cases of a more general distribution. Using this grand canonical approach moments and cumulants, combinants, hierarchical structure, void scaling relations, KNO scaling features, clan variables and branching laws associated with stochastic or ancestral variables are discussed. It is shown that just looking at the mean and fluctuation of data is not enough to distinguish these distributions or the underlying mechanism. A generalization of the Poisson tran...
Pricing of American put options based on a fuzzy binomial model%基于模糊二叉树模型的美式看跌期权定价问题
Institute of Scientific and Technical Information of China (English)
卢丽娟; 胡云姣
2012-01-01
Both randomness and fuzziness should be considered when there is uncertainty in the market. In this paper the volatility of stock price was replaced by parabolic type fuzzy numbers. The fuzzy risk-neutral probabilities were then deduced in order to make a fuzzy binomial model, which is based on the binomial model. The price-setting process of American put options and the optimal exercise times were studied in detail. Furthermore, a numerical example was used to illustrate how to price a single put warrant in the Chinese domestic market. The results indicate that a rational fuzzy option price interval can be evaluated by a fuzzy binomial model and investors can make strategic decisions by changing the confidence levels and parabolic type fuzzy numbers.%市场中影响期权价格的因素具有随机性和模糊性的特点.本文假定股票的价格波动为抛物型模糊数,推导出了模糊风险中性概率,进而将美式期权定价的传统二叉树模型扩展到模糊二叉树模型,给出了该模型的美式看跌期权定价过程和最优实施时间.最后的数值算例将该模型应用到国内的权证市场,针对唯一一只美式认沽权证进行定价分析,结果表明利用模糊二叉树模型定价能够得到一个合理的期权模糊价格区间.投资者可根据自身风险偏好程度改变置信水平和抛物型模糊数来进行投资决策.
Aplicação do modelo binomial na formação de preço de títulos de dívida corporativa no Brasil.
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José Roberto Securato
2008-06-01
Full Text Available Este artigo consiste em uma aplicação do modelo binomial na formação de preços de títulos de dívida e seus componentes – call, conversibilidade, subordinação, senioridade – para uma empresa brasileira. O principal objetivo do trabalho é a adaptação do modelo à realidade brasileira. Os resultados obtidos consistem em estimativas dos preços dos títulos de dívida e da empresa em estudo e comparações com os preços de mercado, procurando identificar oportunidades de compra ou venda desses ativos. Dos seis títulos estudados, três deles apresentaram preços acima do valor de mercado, indicando que o mercado estaria subavaliando o preço desses títulos, enquanto dois outros títulos obtiveram preços abaixo do mercado e um dos títulos praticamente igualou-se ao preço de mercado. O modelo apresentado e suas adaptações indicam a possibilidade de sua aplicação na formação de preço de contratos incompletos avaliando cada uma de suas contingências. Palavras-chave: modelo binominal; avaliação de dívidas; opções reais. Abstract This article presents the implementation of binomial option pricing model to evaluate corporate debt instruments and its components such as call options, convertibility options, seniority and subordination to a Brazilian company. The major results consist of debt securities valuation and its comparison to secondary market prices in order to identify investments opportunities. The paper evaluated six debt securities which have secondary market prices and three of them presented prices above market, two of them were bellow market price and one of them had the same price of the market. The presented model and its adjustments to Brazilian market allow evaluating corporate debt securities and its components, evaluating the impact of new debt issues in the existing ones and comparing debt model and book values. Keywords: binomial model; corporate debt; debt components.
Tang, Wan; Lu, Naiji; Chen, Tian; Wang, Wenjuan; Gunzler, Douglas David; Han, Yu; Tu, Xin M
2015-10-30
Zero-inflated Poisson (ZIP) and negative binomial (ZINB) models are widely used to model zero-inflated count responses. These models extend the Poisson and negative binomial (NB) to address excessive zeros in the count response. By adding a degenerate distribution centered at 0 and interpreting it as describing a non-risk group in the population, the ZIP (ZINB) models a two-component population mixture. As in applications of Poisson and NB, the key difference between ZIP and ZINB is the allowance for overdispersion by the ZINB in its NB component in modeling the count response for the at-risk group. Overdispersion arising in practice too often does not follow the NB, and applications of ZINB to such data yield invalid inference. If sources of overdispersion are known, other parametric models may be used to directly model the overdispersion. Such models too are subject to assumed distributions. Further, this approach may not be applicable if information about the sources of overdispersion is unavailable. In this paper, we propose a distribution-free alternative and compare its performance with these popular parametric models as well as a moment-based approach proposed by Yu et al. [Statistics in Medicine 2013; 32: 2390-2405]. Like the generalized estimating equations, the proposed approach requires no elaborate distribution assumptions. Compared with the approach of Yu et al., it is more robust to overdispersed zero-inflated responses. We illustrate our approach with both simulated and real study data. PMID:26078035
Institute of Scientific and Technical Information of China (English)
王治强; 刘冬元
2013-01-01
In this paper,we extended the classical risk model to a discrete risk model in which the premium rate was a Poisson process and the number of compensation rate was a binomial process. It discussed the nature of surplus process,gave a theorem about the ruin probability and several inferences.%将经典风险模型推广为保费收取为Poisson过程，赔偿次数为二项过程的离散风险模型，讨论了盈余过程的性质，给出了关于破产概率的一个定理和几个推论。
Directory of Open Access Journals (Sweden)
Germán Lobos
2008-12-01
Full Text Available The main objective of this research was to identify the determining factors of the use of public instruments to manage risk in the Chilean wine industry. A binomial logistic regression model was proposed. Based on a survey of 104 viticulture and winemaking companies, a database was constructed between January and October 2007. The model was fitted using maximum likelihood estimation. The variables that turned out to be statistically significant were: risk of the wine price, availability of external consultancy and number of permanent workers. From the Public Management point of view, the main conclusion suggests that the use of public instruments could be increased if viticulturists and winemakers had more external counseling.
Modeling the distribution of new MRI cortical lesions in multiple sclerosis longitudinal studies.
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Maria Pia Sormani
Full Text Available OBJECTIVE: Recent studies have shown the relevance of the cerebral grey matter involvement in multiple sclerosis (MS. The number of new cortical lesions (CLs, detected by specific MRI sequences, has the potential to become a new research outcome in longitudinal MS studies. Aim of this study is to define the statistical model better describing the distribution of new CLs developed over 12 and 24 months in patients with relapsing-remitting (RR MS. METHODS: Four different models were tested (the Poisson, the Negative Binomial, the zero-inflated Poisson and the zero-inflated Negative Binomial on a group of 191 RRMS patients untreated or treated with 3 different disease modifying therapies. Sample size for clinical trials based on this new outcome measure were estimated by a bootstrap resampling technique. RESULTS: The zero-inflated Poisson model gave the best fit, according to the Akaike criterion to the observed distribution of new CLs developed over 12 and 24 months both in each treatment group and in the whole RRMS patients group adjusting for treatment effect. CONCLUSIONS: The sample size calculations based on the zero-inflated Poisson model indicate that randomized clinical trials using this new MRI marker as an outcome are feasible.
Ghosh, Premomoy
2014-01-01
Measured multiplicity distributions of primary charged particles produced in the forward rapidity region of the $proton-proton$ ($pp$) collisions at the centre-of-mass energy, $\\sqrt {s}$ = 7 TeV at the Large Hadron Collider (LHC) have been analyzed in terms of the Negative Binomial Distribution (NBD) function. Like the multiplicity distributions in the mid-rapidity region for the $pp$ collisions at $\\sqrt {s}$ = 7 TeV, the distributions for the minimum bias events in the forward region also are better described with the superposition of two-NBDs, as proposed by a two-component model of particle production from two processes, the "$soft$" and the "$hard$". However, the multiplicity distribution for the "hard-QCD" events in a large pseudorapidity window does not oblige the two-component model.
Dutta, S.; Chan, A. H.; Oh, C. H.
2012-08-01
This paper studies the multiplicity distribution of hadrons produced in p-p collisions at 0.9 and 2.36 TeV using ALICE as a detector. The multiplicity distribution exhibits enhanced void probability. They are also found to satisfy the void probability scaling. The scaling of χ with \\bar n\\bar k2 is studied using the generalized hypergeometric model. The variation of the parameter "a" of the hyper geometric model with energy and type of events is also studied. The parameter "a" distinguishes between various theoretical models, e.g. Lorentz/Catalan, negative binomial, geometric distribution etc. Finally a comparison is made with the p--\\bar p collisions at 200, 546 and 900 GeV. It is observed both for p-p and p--\\bar p data, the value of "a" decreases with increase in collision energy and approach towards the upper bound or the NB model of the void probability scaling.
A three-component description of multiplicity distributions in pp collisions at the LHC
Zborovský, I
2013-01-01
A possible signal of new phenomena emerging in the global characteristics of multiparticle production in hadron interactions at TeV energies is studied. The multiplicity distributions of charged particles measured in proton-proton collisions at the Large Hadron Collider at CERN are analyzed in the phenomenological framework of the weighted superposition of three negative binomial distribution functions. The examination of the experimental data indicates the existence of a narrow peak at low multiplicities which can be described by a separate component in the total distribution. The multiplicity characteristics of the third component reveal approximate energy and pseudorapidity invariance, of which a physical explanation represents a challenging problem in high energy multiple particle production.
French, O. E.
2009-06-01
A random walk model with a negative binomially fluctuating number of steps is considered in the case where the mean of the number fluctuations, \\bar{N} , is finite. The asymptotic behaviour of the resultant statistics in the large \\bar{N} limit is derived and shown to give the K distribution. The equivalence of this model to the hitherto unrelated doubly stochastic representation of the K distribution is also demonstrated. The convergence to the K distribution of the probability density function generated by a random walk with a finite mean number of steps is examined along with the moments, and the non-Gaussian statistics are shown to be a direct result of discreteness and bunching effects.
A three-component description of multiplicity distributions in pp collisions at the LHC
Zborovský, I.
2013-05-01
A possible signal of new phenomena emerging in the global characteristics of multiparticle production in hadron interactions at TeV energies is studied. The multiplicity distributions of charged particles measured in proton-proton collisions at the Large Hadron Collider at CERN are analyzed in the phenomenological framework of the weighted superposition of three negative binomial distribution functions. Examination of the experimental data indicates the existence of a narrow peak at low multiplicities which can be described by a separate component in the total distribution. The multiplicity characteristics of the third component reveal approximate energy and pseudorapidity invariance, of which a physical explanation represents a challenging problem in high energy multiple particle production.
Institute of Scientific and Technical Information of China (English)
Xian-min Geng; Shu-chen Wan
2011-01-01
The compound negative binomial model, introduced in this paper, is a discrete time version. We discuss the Markov properties of the surplus process, and study the ruin probability and the joint distributions of actuarial random vectors in this model. By the strong Markov property and the mass function of a defective renewal sequence, we obtain the explicit expressions of the ruin probability, the finite-horizon ruin probability,the joint distributions of T, U(T - 1), |U(T)| and inf 0≤n＜T1 U(n) (i.e., the time of ruin, the surplus immediately before ruin, the deficit at ruin and maximal deficit from ruin to recovery) and the distributions of some actuariai random vectors.
Directory of Open Access Journals (Sweden)
A. Soemargono
2011-10-01
Full Text Available The spatial distribution of Bactrocera dorsalis complex in the mango orchard that was analyzed using various mathematical indices dispersion and regression models showed an aggregated distribution. Taylor’s power law and Iwao’s regression model fitted well to all data sets. However, Iwao’s regression model fitted the data better, yielding higher values of R2 than Taylor’s power law. As the regression of the reciprocal of k of negative binomial (1/k on [k = ( 2 – s2/n / (s2 – ] was not significant, the calculation of a common k was justified to be 1.30. This implies that the grade of aggregation of the fruit flies population was relatively constant throughout the time despite the variation in sample means. Since the clump size (λ value was more than 2, the aggregated distribution might be due to the behavior and environmental factors working together.
Quantifying the impact of inter-site heterogeneity on the distribution of ChIP-seq data
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Jonathan eCairns
2014-11-01
Full Text Available Chromatin Immunoprecipitation followed by sequencing (ChIP-seq is a valuable tool for epigenetic studies. Analysis of the data arising from ChIP-seq experiments often requires implicit or explicit statistical modelling of the read counts. The simple Poisson model is attractive, but does not provide a good fit to observed ChIP-seq data. Researchers therefore often either extend to a more general model (e.g. the Negative Binomial, and/or exclude regions of the genome that do not conform to the model. Since many modelling strategies employed for ChIP-seq data reduce to fitting a mixture of Poisson distributions, we explore the problem of inferring the optimal mixing distribution. We apply the Constrained Newton Method (CNM, which suggests the Negative Binomial - Negative Binomial (NB-NB mixture model as a candidate for modelling ChIP-seq data. We illustrate fitting the NB-NB model with an accelerated EM algorithm on four data sets from three species. Zero-inflated models have been suggested as an approach to improve model fit for ChIP-seq data. We show that the NB-NB mixture model requires no zero-inflation and suggest that in some cases the need for zero inflation is driven by the model's inability to cope with both artefactual large read counts and the frequently observed very low read counts.We see that the CNM-based approach is a useful diagnostic for the assessment of model fit and inference in ChIP-seq data and beyond. Use of the suggested NB-NB mixture model will be of value not only when calling peaks or otherwise modelling ChIP-seq data, but also when simulating data or constructing blacklists de novo.
DEFF Research Database (Denmark)
Hansen, Klaus Marius; Damm, Christian Heide
2005-01-01
An extension of Knight (2005) that support distributed synchronous collaboration implemented using type-based publish/subscribe......An extension of Knight (2005) that support distributed synchronous collaboration implemented using type-based publish/subscribe...
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Andreas Kyriakoussis
2014-04-01
Full Text Available From Kemp [1], we have a family of confluent q-Chu- Vandermonde distributions, consisted by three members I, II and III, interpreted as a family of q-steady-state distributions from Markov chains. In this article, we provide the moments of the distributions of this family and we establish a continuous limiting behavior for the members I and II, in the sense of pointwise convergence, by applying a q-analogue of the usual Stirling asymptotic formula for the factorial number of order n. Specifically, we initially give the q-factorial moments and the usual moments for the family of confluent q-Chu- Vandermonde distributions and then we designate as a main theorem the conditions under which the confluent q-Chu-Vandermonde distributions I and II converge to a continuous Stieltjes-Wigert distribution. For the member III we give a continuous analogue. Moreover, as applications of this study we present a modified q-Bessel distribution, a generalized q-negative Binomial distribution and a generalized over/underdispersed (O/U distribution. Note that in this article we prove the convergence of a family of discrete distributions to a continuous distribution which is not of a Gaussian type.
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Francisco Ricardo de Toledo
2006-08-01
Full Text Available O estudo da distribuição espacial de pragas é fundamental para elaboração de planos de amostragem para o uso do manejo integrado de pragas. Para o afídeo Toxoptera citricida (Kirkaldy, estudou-se a distribuição espacial em talhões de pomares de citros comerciais de laranja-doce [Citrus sinensis (L. Osbeck] da variedade Pêra, com 5; 9 e 15 anos de idade, durante o período de setembro de 2004 a abril de 2005. Foram realizadas 14 amostragens de número de T. citricida em intervalos aproximados de 15 dias entre as mesmas, utilizando-se de armadilhas adesivas de cor amarela (0,11 x 0,11 m fixadas à planta, a 1,5 m de altura aproximadamente. As armadilhas foram distribuídas na área, a cada cinco plantas na linha, em linhas alternadas, totalizando 137 armadilhas no talhão com 5 anos, 140 no talhão com 9 anos e 80 no talhão com 15 anos. Os índices de dispersão utilizados foram: razão variância média (I, índice de Morisita (Idelta, coeficiente de Green (Cx e expoente k da distribuição Binomial Negativa. O índice que melhor representou a agregação do pulgão foi o expoente k da distribuição Binomial Negativa, e a distribuição binomial negativa foi o modelo que melhor se ajustou aos dados. Através destas análises, verificou-se que a maioria das amostragens apresentou uma distribuição agregada da população de T. citricida.The study of insects' spatial distribution is fundamental to elaborate potential sampling plans to be used in integrated pest management. Spatial distribution of Toxoptera citricida was studied in plots of commercial orange orchards (Citrus sinensis from 'Pêra' variety of 5, 9 and 15 years old, respectively, from September 2004 to April 2005. It was carried through 14 fortnightlies Toxoptera citricida samplings numbers, utilizing yellow adhesive traps (0.11 x 0.11 m settled on the plant at 1.5 m of height approximately. The traps were distributed in the area each five plants in the line, in alternated
Football fever: self-affirmation model for goal distributions
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W. Janke
2009-01-01
Full Text Available The outcome of football games, as well as matches of most other popular team sports, depends on a combination of the skills of players and coaches and a number of external factors which, due to their complex nature, are presumably best viewed as random. Such parameters include the unpredictabilities of playing the ball, the players' shape of the day or environmental conditions such as the weather and the behavior of the audience. Under such circumstances, it appears worthwhile to analyze football score data with the toolbox of mathematical statistics in order to separate deterministic from stochastic effects and see what impact the cooperative and social nature of the "agents" of the system has on the resulting stochastic observables. Considering the probability distributions of scored goals for the home and away teams, it turns out that especially the tails of the distributions are not well described by the Poissonian or binomial model resulting from the assumption of uncorrelated random events. On the contrary, some more specific probability densities such as those discussed in the context of extreme-value statistics or the so-called negative binomial distribution fit these data rather well. There seemed to be no good argument to date, however, why the simplest Poissonian model fails and, instead, the latter distributions should be observed. To fill this gap, we introduced a number of microscopic models for the scoring behavior, resulting in a Bernoulli random process with a simple component of self-affirmation. These models allow us to represent the observed probability distributions surprisingly well, and the phenomenological distributions used earlier can be understood as special cases within this framework. We analyzed historical football score data from many leagues in Europe as well as from international tournaments, including data from all past tournaments of the "FIFA World Cup" series, and found the proposed models to be applicable in
Risk Families and the Unequal Distribution of Deaths in France and Sweden during the 19th Century
DEFF Research Database (Denmark)
Torres, Catalina; oeppen, James; Jacobsen, Rune;
2016-01-01
need of shifting the attention from single individuals to families as the appropriate units of analysis in the study of infant and child mortality (Edvinsson and Janssens 2012). In the present study, we use aggregate mortality data as well as two reliable sources of historical microdata from Sweden and...... Lorenz curves, where the observed distributions of deaths will be compared with the corresponding expected binomial distributions. The impact of several factors affecting the distribution of infant and child deaths within families will be analysed with logistic regression, with the mothers as the units...... of analysis. We expect to find higher levels of death clustering in populations with high mortality. Furthermore, we expect the distribution of deaths to be determined by differences in various biological as well as social characteristics of the mother, in particular the length of the birth interval...
Elizalde, E.; Gaztanaga, E.
1992-01-01
The dependence of counts in cells on the shape of the cell for the large scale galaxy distribution is studied. A very concrete prediction can be done concerning the void distribution for scale invariant models. The prediction is tested on a sample of the CfA catalog, and good agreement is found. It is observed that the probability of a cell to be occupied is bigger for some elongated cells. A phenomenological scale invariant model for the observed distribution of the counts in cells, an extension of the negative binomial distribution, is presented in order to illustrate how this dependence can be quantitatively determined. An original, intuitive derivation of this model is presented.
Roxin, Alex
2011-01-01
Neuronal network models often assume a fixed probability of connection between neurons. This assumption leads to random networks with binomial in-degree and out-degree distributions which are relatively narrow. Here I study the effect of broad degree distributions on network dynamics by interpolating between a binomial and a truncated power-law distribution for the in-degree and out-degree independently. This is done both for an inhibitory network (I network) as well as for the recurrent excitatory connections in a network of excitatory and inhibitory neurons (EI network). In both cases increasing the width of the in-degree distribution affects the global state of the network by driving transitions between asynchronous behavior and oscillations. This effect is reproduced in a simplified rate model which includes the heterogeneity in neuronal input due to the in-degree of cells. On the other hand, broadening the out-degree distribution is shown to increase the fraction of common inputs to pairs of neurons. This leads to increases in the amplitude of the cross-correlation (CC) of synaptic currents. In the case of the I network, despite strong oscillatory CCs in the currents, CCs of the membrane potential are low due to filtering and reset effects, leading to very weak CCs of the spike-count. In the asynchronous regime of the EI network, broadening the out-degree increases the amplitude of CCs in the recurrent excitatory currents, while CC of the total current is essentially unaffected as are pairwise spiking correlations. This is due to a dynamic balance between excitatory and inhibitory synaptic currents. In the oscillatory regime, changes in the out-degree can have a large effect on spiking correlations and even on the qualitative dynamical state of the network. PMID:21556129
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Marilia Gregolin Costa
2010-10-01
Full Text Available The psyllid Diaphorina citri Kuwayama is one of the most important pests of citrus, mainly because it is the vector of the bacterium that causes huanglongbing (HLB or 'Greening' disease. To study the spatial distribution of nymphs and adults of this pest, an experiment was carried out in two 'Valencia' sweet orange orchards, four and 12 years of age, established in Matão, central area of São Paulo state, Brazil. The following dispersion indices were used to study pest aggregation in the citrus plants: variance/mean relationship (I, index of Morisita (Iδ, coefficient of Green (Cx, the exponent of negative binomial distribution, common k (c and Taylor's Power Law for each sampling. The negative binomial distribution was more representative of the spatial distribution of this psyllid, for both nymphs and adults. For most samplings, psyllid nymphs found in branches and adults caught in traps had an aggregated distribution.O psilídeo Diaphorina citri Kuwayama tornou-se nos últimos anos uma das mais importantes pragas na cultura de citros, principalmente pelos prejuízos causados às plantas por ser o transmissor da bactéria causadora da doença Huanglongbing (HLB ou 'Greening'. Com a finalidade de estudar a distribuição espacial de ninfas e adultos desta praga, instalaram-se experimentos em duas áreas de citros com histórico de ocorrência de HLB, no município de Matão (região central do Estado de São Paulo, em plantas de laranja 'Valência', com quatro e 12 anos de idade. Para estudo da agregação da população nas plantas, foram utilizados os seguintes índices de dispersão: razão variância/média (I, índice de Morisita (Iδ, coeficiente de Green (Cx e expoente da distribuição binomial negativa, k comum (c e lei da potência de Taylor para cada amostragem. A distribuição binomial negativa foi o modelo mais adequado para representar a distribuição espacial do psilídeo, tanto para ninfas como para adultos. Na maioria das
Institute of Scientific and Technical Information of China (English)
徐晟; 徐媛; 赵惠芳
2010-01-01
文章在泊松分布评价模型改进的基础上提出了负二项分布的评价模型,对我国区域自主创新进行评价,充分考虑了影响区域自主创新的因素,并将这些凶素纳入到评价模型中;实验研究结果表明,负二项分布模型运用于区域自丰创新的评价是可行和有效的,为国家和区域自主创新的评价提供了一个新的研究工具.
Institute of Scientific and Technical Information of China (English)
田俊忠
2001-01-01
通过讨论负二项分布族的充分完备统计量,可给出未知参数θ的一致最小方差无偏估计,并通过Cramer-Rao不等式及其无偏估计下界的讨论,证明了θ的惟一的UMVU估计是渐近有效估计.
Institute of Scientific and Technical Information of China (English)
严水仙; 高淑京
2015-01-01
本文给出了负二项分布两种不同定义下概率母函数,利用两种不同的方法计算出概率母函数的表达式,最后解释了纯生过程服从负二项分布及其生物学意义.
Institute of Scientific and Technical Information of China (English)
苏清华; 刘次华
2009-01-01
对负二项分布,给出可靠度在熵损失函数下的Bayes估计,在此基础上给出当先验分布为幂分布时,可靠度的E-Bayes估计和多层Bayes估计,并设计了相应的数值实验,实验结果表明负二项分布可靠度的E-Bayes估计较多层Bayes估计稳健性更好,计算更简单,便于实际应用.
Institute of Scientific and Technical Information of China (English)
董云; 丁芳清
2013-01-01
引入随机序列滑动似然比作为整值随机变量序列相对于服从负二项分布的独立随机变量序列的偏差的一种随机性度量,通过滑动相对熵限定了样本空间的一个子集.在此子集上得到了一类关于任意整值随机变量序列的用不等式表示的定理,即强偏差定理.
Institute of Scientific and Technical Information of China (English)
计宏伟; 孔繁亮
2010-01-01
考虑了保费、理赔支付时间为离散时间的风险模型,根据寿险保险实际情况,研究了带有利率、通货膨胀率及带退保单因素的负二项风险模型及其盈余的性质. 应用鞅分析方法,探讨了由该风险模型得到的破产概率的一个表达式.
Institute of Scientific and Technical Information of China (English)
孟生旺; 袁卫
2001-01-01
@@ 一、引言 在世界上任何一个国家,几乎所有的汽车保险人都采用了无赔款优待系统,即所谓的BMS(BonusMalus System).在该系统中,保险公司将根据投保人以往年份的索赔情况调整其续期保费.通常的原则是,上一保险年度发生的索赔次数越多,次年的续期保费将越高.反之,如果上一保险年度没有发生索赔,保险公司将降低投保人的续期保费.毫无疑问,保险公司调整投保人续期保费的主要目的之一就是为了公平投保人的保费负担,使高风险的投保人缴纳相对较高的保险费.但是,实证研究结果表明(参见文献[1]),保险公司目前应用的这些系统(包括我国的在内)往往难以达到这一目的.
Institute of Scientific and Technical Information of China (English)
王芃芃; 王燕婷; 江一鸣
2013-01-01
将经典风险理论中的复合泊松模型调整为复合负二项模型,考虑索赔次数服从负二项分布的情况,得到初始资本为u的破产概率表达式.并以索赔额服从指数分布为例,给出破产概率的近似解.
负二项分布中未知参数p的一个区间估计%An interval estimation of unknown parameter p in negative binomial distribution
Institute of Scientific and Technical Information of China (English)
王晓红; 康乐; 宋立新
2009-01-01
讨论了负二项分布的最大试验次数,并用所得到的最大试验次数给出负二项分布中未知参数户的一个较为理想的区间估计.解决了负二项分布在小样本试验下未知参数户的区间估计问题.
Institute of Scientific and Technical Information of China (English)
程维虎; 王莉丽
2004-01-01
负二项分布在昆虫空间分布中有重要应用,其参数常用矩法或零频率法来估计.本文讨论两种估计的性质,得到大样本情形下,零频率较大时,零频率估计较矩估计有更高精度的结论; 通过计算机模拟,验证结论.
Multiplicity distribution in p+p collisions at LHC energies
Dash, Ajay Kumar
2009-01-01
multiplicity distributions by Negative Binomial Distributions (NBD) at lower \\sqrt(s) to hold for LHC energies, we observe that the logarithmic \\sqrt(s) dependence of are favored by the models at midrapidity. The dN_ch/deta versus \\eta for the existing measurements are found to be reasonably well described by The multiplicity (N_ch) and pseudorapidity distribution (dN_ch/deta) of charged particles in p+p collisions at Large Hadron Collider (LHC) energies of \\sqrt(s) = 10 and 14 TeV are obtained from extrapolation of existing measurements at lower \\sqrt(s). These distributions are then compared to calculations from PYTHIA and PHOJET models. The existing \\sqrt(s) measurements are unable to distinguish between a logarithmic and power law dependence of the average charged particle multiplicity () on \\sqrt(s), and their extrapolation to energies accessible at LHC give very different values. Assuming a reasonably good description of inclusive charged particle a function with three parameters which accounts for the...
Self-affirmation model for football goal distributions
Bittner, E.; Nußbaumer, A.; Janke, W.; Weigel, M.
2007-06-01
Analyzing football score data with statistical techniques, we investigate how the highly co-operative nature of the game is reflected in averaged properties such as the distributions of scored goals for the home and away teams. It turns out that in particular the tails of the distributions are not well described by independent Bernoulli trials, but rather well modeled by negative binomial or generalized extreme value distributions. To understand this behavior from first principles, we suggest to modify the Bernoulli random process to include a simple component of self-affirmation which seems to describe the data surprisingly well and allows to interpret the observed deviation from Gaussian statistics. The phenomenological distributions used before can be understood as special cases within this framework. We analyzed historical football score data from many leagues in Europe as well as from international tournaments and found the proposed models to be applicable rather universally. In particular, here we compare men's and women's leagues and the separate German leagues during the cold war times and find some remarkable differences.
Statistical distributions of earthquake numbers: consequence of branching process
Kagan, Yan Y.
2010-03-01
We discuss various statistical distributions of earthquake numbers. Previously, we derived several discrete distributions to describe earthquake numbers for the branching model of earthquake occurrence: these distributions are the Poisson, geometric, logarithmic and the negative binomial (NBD). The theoretical model is the `birth and immigration' population process. The first three distributions above can be considered special cases of the NBD. In particular, a point branching process along the magnitude (or log seismic moment) axis with independent events (immigrants) explains the magnitude/moment-frequency relation and the NBD of earthquake counts in large time/space windows, as well as the dependence of the NBD parameters on the magnitude threshold (magnitude of an earthquake catalogue completeness). We discuss applying these distributions, especially the NBD, to approximate event numbers in earthquake catalogues. There are many different representations of the NBD. Most can be traced either to the Pascal distribution or to the mixture of the Poisson distribution with the gamma law. We discuss advantages and drawbacks of both representations for statistical analysis of earthquake catalogues. We also consider applying the NBD to earthquake forecasts and describe the limits of the application for the given equations. In contrast to the one-parameter Poisson distribution so widely used to describe earthquake occurrence, the NBD has two parameters. The second parameter can be used to characterize clustering or overdispersion of a process. We determine the parameter values and their uncertainties for several local and global catalogues, and their subdivisions in various time intervals, magnitude thresholds, spatial windows, and tectonic categories. The theoretical model of how the clustering parameter depends on the corner (maximum) magnitude can be used to predict future earthquake number distribution in regions where very large earthquakes have not yet occurred.
Institute of Scientific and Technical Information of China (English)
雷汉云
2014-01-01
实物期权估值(ROV)方法在不确定条件下最优投资决策的应用是一种非常有价值的方法，但由于其复杂的计算，在采矿业的实际应用一直比较缓慢。针对传统的净现值法和实物期权法在矿业权评估的缺陷，从探矿权项目股权收购方的角度出发，通过探矿权转让协议如何作为一系列连续复合实物期权估算其价值的实例，采用二项式网格方法和风险中性概率计算探矿权中标的资产相应各期的期权价值，以期为现实的探矿权转让协议中评估更复杂的连续时间复合实物期权提供一个新的视角。%Real options valuation (ROV) method is a very valuable method for optimal investment decisions under conditions of uncertainty, but it has been used for the practical application of the mining industry slowly because of its complex calculations. With the development of binomial grid method, it is simplified and has been applied to daily financial evaluation and decision-making under conditions of uncertainty in recent years. We use the binomial method and risk-neutral probability to calculate each of option value of the assets on the acquirer’s equity interest in the project, by an example How to Transfer Agreement by prospecting complex as a series of successive instances of real options to estimate their value. Our purpose is to provide a new perspective for assessing more complex transfer agreement in continuous time compound real option.
Institute of Scientific and Technical Information of China (English)
无
2004-01-01
Distribution center is a logistics link fulfill physical distribution as its main functionGenerally speaking, it's a large and hiahly automated center destined to receive goods from various plants and suppliers,take orders,fill them efficiently,and deliver goods to customers as quickly as possible.
Institute of Scientific and Technical Information of China (English)
张铁军; 唐琤琤; 康云霞
2012-01-01
针对我国交通事故呈现出的在公路穿村镇路段聚集的趋势,在某山岭地形区域进行了双车道公路的交通事故、交通组成、道路和路侧等因素的大量数据采集,并对公路穿村镇路段的整体安全特性进行了分析,采用负二项模型等事故预测模型和相关检验理论对模型形式,以及公路穿村镇路段全部事故和追尾、碰撞、路侧等不同形态的事故规律特性进行了深入分析.研究结果发现,公路穿村镇路段的事故时空分布呈一定规律性；交通量、混杂率和道路横坡度为影响公路穿村镇路段交通安全的3个显著因素,且均呈正向影响.%Aimed at the aggregating trend of traffic accidents in highway sections passing through towns/ villages in China, a large number of two-lane highway safety data, such as traffic accident, traffic composition, highway and roadside factors were collected in a mountainous area. Moreover, the overall safety characteristics of town/village accidents were analyzed, and the accident prediction model such as negative binomial prediction model and relative test methods were used to deeply analyze the model form and the regularities of total accidents, collision, rear-ended crash, roadside accident, etc. It is found that (1) the accidents in road sections passing through towns/villages are in the regular temporal and special distribution; (2) truck proportion, traffic volume and cross slope are the significant factors influencing traffic safety of road sections passing through towns/villages, and all of them are positive in such sections.
Generalized Poisson-Lindely Distribution in Promotion Time Cure Model
Directory of Open Access Journals (Sweden)
Ahmad Reza Baghestani
2014-12-01
Full Text Available 1024x768 Long-term survival analysis has been improved in the last decade and most of the models concentrate on the promotion time cure model that proposed by Chen (1999. These models are based on the distribution of latent variable N, number of initiated node cells. In this paper we proposed a Generalized Poisson-Lindely distribution that is another option instead of Negative Binomial distribution when there is overdispersion. The results indicated a better fitness compared to others, because of its more flexibility. Parameter estimation has been done by Bayesian approach, in a real data set and a simulation study has shown the advantages of proposed model. Normal 0 false false false /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman"; mso-ansi-language:#0400; mso-fareast-language:#0400; mso-bidi-language:#0400;}
Directory of Open Access Journals (Sweden)
Saad T. Bakir
2012-01-01
Full Text Available This paper develops a distribution-free (or nonparametric Shewhart-type statistical quality control chart for detecting a broad change in the probability distribution of a process. The proposed chart is designed for grouped observations, and it requires the availability of a reference (or training sample of observations taken when the process was operating in-control. The charting statistic is a modified version of the two-sample Kolmogorov-Smirnov test statistic that allows the exact calculation of the conditional average run length using the binomial distribution. Unlike the traditional distribution-based control charts (such as the Shewhart X-Bar, the proposed chart maintains the same control limits and the in-control average run length over the class of all (symmetric or asymmetric continuous probability distributions. The proposed chart aims at monitoring a broad, rather than a one-parameter, change in a process distribution. Simulation studies show that the chart is more robust against increased skewness and/or outliers in the process output. Further, the proposed chart is shown to be more efficient than the Shewhart X-Bar chart when the underlying process distribution has tails heavier than those of the normal distribution.
Extrapolation of multiplicity distribution in p+p(\\bar{p}) collisions to LHC energies
Dash, Ajay Kumar; Mohanty, Bedangadas
2010-02-01
The multiplicity (Nch) and pseudorapidity distribution (dNch/dη) of primary charged particles in p + p collisions at Large Hadron Collider (LHC) energies of \\sqrt{s} = 10 and 14 TeV are obtained from extrapolation of existing measurements at lower \\sqrt{s}. These distributions are then compared to calculations from PYTHIA and PHOJET models. The existing \\sqrt{s} measurements are unable to distinguish between a logarithmic and power law dependence of the average charged particle multiplicity (langNchrang) on \\sqrt{s}, and their extrapolation to energies accessible at LHC give very different values. Assuming a reasonably good description of inclusive charged particle multiplicity distributions by negative binomial distribution (NBD) at lower \\sqrt{s} to hold for LHC energies, we observe that the logarithmic \\sqrt{s} dependences of langNchrang are favored by the models at midrapidity. The dNch/dη versus η distributions for the existing measurements are found to be reasonably well described by a function with three parameters which accounts for the basic features of the distribution, height at midrapidity, central rapidity plateau and the higher rapidity fall-off. Extrapolation of these parameters as a function of \\sqrt{s} is used to predict the pseudorapidity distributions of charged particles at LHC energies. dNch/dη calculations from PYTHIA and PHOJET models are found to be lower compared to those obtained from the extrapolated dNch/dη versus η distributions for a broad η range.
Knight, C
2012-01-01
This article explores the Rawlsian goal of ensuring that distributions are not influenced by the morally arbitrary. It does so by bringing discussions of distributive justice into contact with the debate over moral luck initiated by Williams and Nagel. Rawls’ own justice as fairness appears to be incompatible with the arbitrariness commitment, as it creates some equalities arbitrarily. A major rival, Dworkin’s version of brute luck egalitarianism, aims to be continuous wi...
Energy Technology Data Exchange (ETDEWEB)
Tison, R.R.; Baker, N.R.; Blazek, C.F.
1979-07-01
Distribution of fuel is considered from a supply point to the secondary conversion sites and ultimate end users. All distribution is intracity with the maximum distance between the supply point and end-use site generally considered to be 15 mi. The fuels discussed are: coal or coal-like solids, methanol, No. 2 fuel oil, No. 6 fuel oil, high-Btu gas, medium-Btu gas, and low-Btu gas. Although the fuel state, i.e., gas, liquid, etc., can have a major impact on the distribution system, the source of these fuels (e.g., naturally-occurring or coal-derived) does not. Single-source, single-termination point and single-source, multi-termination point systems for liquid, gaseous, and solid fuel distribution are considered. Transport modes and the fuels associated with each mode are: by truck - coal, methanol, No. 2 fuel oil, and No. 6 fuel oil; and by pipeline - coal, methane, No. 2 fuel oil, No. 6 oil, high-Btu gas, medium-Btu gas, and low-Btu gas. Data provided for each distribution system include component makeup and initial costs.
DEFF Research Database (Denmark)
Glaveanu, Vlad Petre
This book challenges the standard view that creativity comes only from within an individual by arguing that creativity also exists ‘outside’ of the mind or more precisely, that the human mind extends through the means of action into the world. The notion of ‘distributed creativity’ is not commonly...... used within the literature and yet it has the potential to revolutionise the way we think about creativity, from how we define and measure it to what we can practically do to foster and develop creativity. Drawing on cultural psychology, ecological psychology and advances in cognitive science, this...... book offers a basic framework for the study of distributed creativity that considers three main dimensions of creative work: sociality, materiality and temporality. Starting from the premise that creativity is distributed between people, between people and objects and across time, the book reviews...
Testing the anisotropy in the angular distribution of $Fermi$/GBM gamma-ray bursts
Tarnopolski, Mariusz
2015-01-01
Gamma-ray bursts (GRBs) were confirmed to be of extragalactic origin due to their isotropic angular distribution, combined with the fact that they exhibited an intensity distribution that deviated strongly from the $-3/2$ power law. This finding was later confirmed with the first redshift, equal to at least $z=0.835$, measured for GRB970508. Despite this result, the data from $CGRO$/BATSE and $Swift$/BAT indicate that long GRBs are indeed distributed isotropically, but the distribution of short GRBs is anisotropic. $Fermi$/GBM has detected 1669 GRBs up to date, and their sky distribution is examined in this paper. A number of statistical tests is applied: nearest neighbour analysis, fractal dimension, dipole and quadrupole moments of the distribution function decomposed into spherical harmonics, binomial test, and the two point angular correlation function. Monte Carlo benchmark testing of each test is performed in order to evaluate its reliability. It is found that short GRBs are distributed anisotropically ...
带反方向视角和二项交叉的布谷鸟搜索算法%Cuckoo Search Algorithm with Reverse Direction Angle and Binomial Crossover
Institute of Scientific and Technical Information of China (English)
梁忠; 林要华; 周术诚
2015-01-01
Cuckoo search algorithm is a new nature-inspired optimization technique, which uses Lévy Flights random walk and Biased random walk to search new solutions iteratively. In Lévy Flights random walk, all individuals search new solutions around the best solution obtained so far. This may easy make the population converge to the best one. To avoid converging to the current optimal solution, this paper uses the reverse direction angle strategy to search new solutions probably, and proposes a cuckoo search algorithm with reverse direction angle and binomial crossover, called RBCS. In RBCS, a binomial crossover strategy is employed to enhance the search ability of Biased random walk. Compared with the standard cuckoo search algorithm, the experimental results show that the proposed strategies can improve the convergence speed and the solution quality of the algorithm for the continuous function optimization problems effectively. Compared with other improved cuckoo search algorithms and other evolutionary algorithms, the experimental results reveal that the proposed algorithm is competitive for the continuous function optimization problems.%布谷鸟搜索算法是一种新兴的自然仿生优化技术，其借用Lévy Flights随机走动和Biased随机走动搜索新的解。在Lévy Flights随机走动中，所有个体以当前种群获得的最优解为导向进行搜索，这容易导致种群趋同于该最优解。针对此问题，引入反方向视角使种群基于一定概率反向搜索，以避免趋同于当前最优解，并提出带反方向视角和二项式交叉的布谷鸟搜索算法。在提出的算法中，借用二项交叉操作以提高Biased随机走动的搜索能力。与标准的布谷鸟搜索算法对比，实验结果说明提出的策略能够有效地改善布谷鸟搜索算法求解连续函数优化问题的收敛速度和解的质量。与其他改进的布谷鸟搜索算法以及其他进化算法对比，实验结果说明提出
DEFF Research Database (Denmark)
Borregaard, Michael Krabbe; Hendrichsen, Ditte Katrine; Nachman, Gøsta Støger
2008-01-01
, depending on the nature of intraspecific interactions between them: while the individuals of some species repel each other and partition the available area, others form groups of varying size, determined by the fitness of each group member. The spatial distribution pattern of individuals again strongly...
Directory of Open Access Journals (Sweden)
Meaghan A. Labine
2015-11-01
Full Text Available Background: The incidence of liver cancer has been increasing in Canada over the past decade, as has cyanobacterial contamination of Canadian freshwater lakes and drinking water sources. Cyanotoxins released by cyanobacteria have been implicated in the pathogenesis of liver cancer. Objective: To determine whether a geographic association exists between liver cancer and surrogate markers of cyanobacterial contamination of freshwater lakes in Canada. Methods: A negative binomial regression model was employed based on previously identified risk factors for liver cancer. Results: No association existed between the geographic distribution of liver cancer and surrogate markers of cyanobacterial contamination. As predicted, significant associations existed in areas with a high prevalence of hepatitis B virus infection, large immigrant populations and urban residences. Discussion and Conclusions: The results of this study suggest that cyanobacterial contamination of freshwater lakes does not play an important role in the increasing incidence of liver cancer in Canada.
,
2014-01-01
We report the first measurements of the moments -mean ($M$), variance ($\\sigma^{2}$), skewness ($S$) and kurtosis ($\\kappa$) -of the net-charge multiplicity distributions at mid-rapidity in Au+Au collisions at seven energies, ranging from $\\sqrt {{s_{\\rm NN}}}$=7.7 to 200 GeV, as a part of the Beam Energy Scan program at RHIC. The moments are related to the thermodynamic susceptibilities of net-charge, which are expected to diverge at the QCD critical point. We compare the products of the moments, $\\sigma^{2}/M$, $S\\sigma$ and $\\kappa\\sigma^{2}$ with the expectations from Poisson and negative binomial distributions (NBD). The $S\\sigma$ values deviate from Poisson and are close to NBD baseline, while the $\\kappa\\sigma^{2}$ values tend to lie between the two. Within the present uncertainties, our data do not show clear evidence of non-monotonic behavior as a function of collision energy.
Chau, L L; Chau, Ling-Lie; Huang, Ding-Wei
1993-01-01
We have derived explicit expressions in the 1-d Ising model for multiplicity distributions $P_{\\del\\xi}(n)$ and factorial moments $F_q(\\del\\xi)$. We identify the salient features of $P_{\\del\\xi}(n)$ that lead to scaling, $F_q(\\del\\xi)=\\F_q[F_2]$, and universality. These results compare well with the presently available high-energy data of $\\bar{p}p$ and $e^+e^-$ reactions. We point out the important features that should be studied in future higher-energy experiments of multiparticle productions in $pp$, $\\bar{p}p$, $ep$, $e^+e^-$, and $NN$. We also make comments on comparisons with KNO and negative-binomial distributions.
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Sara Soto-De Leon
Full Text Available BACKGROUND: Infection with multiple types of human papillomavirus (HPV is one of the main risk factors associated with the development of cervical lesions. In this study, cervical samples collected from 1,810 women with diverse sociocultural backgrounds, who attended to their cervical screening program in different geographical regions of Colombia, were examined for the presence of cervical lesions and HPV by Papanicolau testing and DNA PCR detection, respectively. PRINCIPAL FINDINGS: The negative binomial distribution model used in this study showed differences between the observed and expected values within some risk factor categories analyzed. Particularly in the case of single infection and coinfection with more than 4 HPV types, observed frequencies were smaller than expected, while the number of women infected with 2 to 4 viral types were higher than expected. Data analysis according to a negative binomial regression showed an increase in the risk of acquiring more HPV types in women who were of indigenous ethnicity (+37.8%, while this risk decreased in women who had given birth more than 4 times (-31.1%, or were of mestizo (-24.6% or black (-40.9% ethnicity. CONCLUSIONS: According to a theoretical probability distribution, the observed number of women having either a single infection or more than 4 viral types was smaller than expected, while for those infected with 2-4 HPV types it was larger than expected. Taking into account that this study showed a higher HPV coinfection rate in the indigenous ethnicity, the role of underlying factors should be assessed in detail in future studies.
Soto-De Leon, Sara; Camargo, Milena; Sanchez, Ricardo; Munoz, Marina; Perez-Prados, Antonio; Purroy, Antonio; Patarroyo, Manuel Elkin; Patarroyo, Manuel Alfonso
2011-01-01
Background Infection with multiple types of human papillomavirus (HPV) is one of the main risk factors associated with the development of cervical lesions. In this study, cervical samples collected from 1,810 women with diverse sociocultural backgrounds, who attended to their cervical screening program in different geographical regions of Colombia, were examined for the presence of cervical lesions and HPV by Papanicolau testing and DNA PCR detection, respectively. Principal Findings The negative binomial distribution model used in this study showed differences between the observed and expected values within some risk factor categories analyzed. Particularly in the case of single infection and coinfection with more than 4 HPV types, observed frequencies were smaller than expected, while the number of women infected with 2 to 4 viral types were higher than expected. Data analysis according to a negative binomial regression showed an increase in the risk of acquiring more HPV types in women who were of indigenous ethnicity (+37.8%), while this risk decreased in women who had given birth more than 4 times (−31.1%), or were of mestizo (−24.6%) or black (−40.9%) ethnicity. Conclusions According to a theoretical probability distribution, the observed number of women having either a single infection or more than 4 viral types was smaller than expected, while for those infected with 2–4 HPV types it was larger than expected. Taking into account that this study showed a higher HPV coinfection rate in the indigenous ethnicity, the role of underlying factors should be assessed in detail in future studies. PMID:21379574
Quasihomogeneous distributions
von Grudzinski, O
1991-01-01
This is a systematic exposition of the basics of the theory of quasihomogeneous (in particular, homogeneous) functions and distributions (generalized functions). A major theme is the method of taking quasihomogeneous averages. It serves as the central tool for the study of the solvability of quasihomogeneous multiplication equations and of quasihomogeneous partial differential equations with constant coefficients. Necessary and sufficient conditions for solvability are given. Several examples are treated in detail, among them the heat and the Schrödinger equation. The final chapter is devoted to quasihomogeneous wave front sets and their application to the description of singularities of quasihomogeneous distributions, in particular to quasihomogeneous fundamental solutions of the heat and of the Schrödinger equation.
Directory of Open Access Journals (Sweden)
Luca Ferreri
2014-11-01
Full Text Available The spread of tick-borne pathogens represents an important threat to human and animal health in many parts of Eurasia. Here, we analysed a 9-year time series of Ixodes ricinus ticks feeding on Apodemus flavicollis mice (main reservoir-competent host for tick-borne encephalitis, TBE sampled in Trentino (Northern Italy. The tail of the distribution of the number of ticks per host was fitted by three theoretical distributions: Negative Binomial (NB, Poisson-LogNormal (PoiLN, and Power-Law (PL. The fit with theoretical distributions indicated that the tail of the tick infestation pattern on mice is better described by the PL distribution. Moreover, we found that the tail of the distribution significantly changes with seasonal variations in host abundance. In order to investigate the effect of different tails of tick distribution on the invasion of a non-systemically transmitted pathogen, we simulated the transmission of a TBE-like virus between susceptible and infective ticks using a stochastic model. Model simulations indicated different outcomes of disease spreading when considering different distribution laws of ticks among hosts. Specifically, we found that the epidemic threshold and the prevalence equilibria obtained in epidemiological simulations with PL distribution are a good approximation of those observed in simulations feed by the empirical distribution. Moreover, we also found that the epidemic threshold for disease invasion was lower when considering the seasonal variation of tick aggregation.
Institute of Scientific and Technical Information of China (English)
孙建伟; 许汴利; 陈豪敏
2011-01-01
目的 研究狂犬病病例在河南省县区层面空间分布状态及动态变化.方法 对河南省2004-2010年狂犬病县区层面疫情数据进行收集和整理,进行Poisson分布和负二项分布的拟合与检验,分析聚集特征及变化.结果 按照α=0.05水平,2004、2005、2007和2009年狂犬病病例在县区层面服从负二项分布而不服从P0isson分布(P＜0.001);2008和2010年更倾向于服从负二项分布,但同时不排除服从Poisson分布;2006年两种分布均不服从.从负二项聚集性参数k值来看,狂犬病病例在县区层面的聚集程度从2004-2008年逐年降低,2009年有所增强,2010年又呈现聚集性减弱倾向.聚集程度与疫情县区平均病例数呈正相关(r=0.807,P=0.028).结论 狂犬病病例在河南省县区层面的分布更倾向于负二项分布,具有一定程度的空间聚集性,但聚集程度有逐年下降趋势.%Objective To study the spatial distribution and dynamics of human rabies cases at the county level, in Henan province to provide scientific evidence for the development of control program on rabies. Methods Data of human rabies cases at the county level from 2004 to 2010 in Henan province were analyzed by Poisson distribution and negative binomial distribution. Data calculation was conducted manually. Results According to the level of α =0.05 being set, there were three different results appeared: the first was fitted negative binomial distribution in 2004, 2005,2007 and 2009; the second was prioritized negative binomial distribution, but the poisson distribution could not be excluded in 2008 and 2010; the last one was fitted neither negative binomial distribution nor poisson distribution in 2006. By the clustering parameter k, the clustering degree at county level decreased from 2004 to 2008, then ascending in 2009 but descending again in 2010. The degree of clustering showed a positive correlation with the county mean cases in the prevalent counties (r=0.807,P=0
Cyclotomy of Weil Sums of Binomials
Aubry, Yves; Katz, Daniel J.; Langevin, Philippe
2013-01-01
The Weil sum $W_{K,d}(a)=\\sum_{x \\in K} \\psi(x^d + a x)$ where $K$ is a finite field, $\\psi$ is an additive character of $K$, $d$ is coprime to $|K^\\times|$, and $a \\in K^\\times$ arises often in number-theoretic calculations, and in applications to finite geometry, cryptography, digital sequence design, and coding theory. Researchers are especially interested in the case where $W_{K,d}(a)$ assumes three distinct values as $a$ runs through $K^\\times$. A Galois-theoretic approach, combined with...
Monomials, Binomials, and Riemann-Roch
Manjunath, Madhusudan; Sturmfels, Bernd
2012-01-01
The Riemann-Roch theorem on a graph G is related to Alexander duality in combinatorial commutive algebra. We study the lattice ideal given by chip firing on G and the initial ideal whose standard monomials are the G-parking functions. When G is a saturated graph, these ideals are generic and the Scarf complex is a minimal free resolution. Otherwise, syzygies are obtained by degeneration. We also develop a self-contained Riemann-Roch theory for artinian monomial ideals.
Adare, A.; Afanasiev, S.; Aidala, C.; Ajitanand, N. N.; Akiba, Y.; Akimoto, R.; Al-Bataineh, H.; Alexander, J.; Al-Ta'Ani, H.; Angerami, A.; Aoki, K.; Apadula, N.; Aramaki, Y.; Asano, H.; Aschenauer, E. C.; Atomssa, E. T.; Averbeck, R.; Awes, T. C.; Azmoun, B.; Babintsev, V.; Bai, M.; Baksay, G.; Baksay, L.; Bannier, B.; Barish, K. N.; Bassalleck, B.; Basye, A. T.; Bathe, S.; Baublis, V.; Baumann, C.; Baumgart, S.; Bazilevsky, A.; Belikov, S.; Belmont, R.; Bennett, R.; Berdnikov, A.; Berdnikov, Y.; Bickley, A. A.; Black, D.; Blau, D. S.; Bok, J. S.; Boyle, K.; Brooks, M. L.; Bryslawskyj, J.; Buesching, H.; Bumazhnov, V.; Bunce, G.; Butsyk, S.; Camacho, C. M.; Campbell, S.; Castera, P.; Chen, C.-H.; Chi, C. Y.; Chiu, M.; Choi, I. J.; Choi, J. B.; Choi, S.; Choudhury, R. K.; Christiansen, P.; Chujo, T.; Chung, P.; Chvala, O.; Cianciolo, V.; Citron, Z.; Cole, B. A.; Connors, M.; Constantin, P.; Cronin, N.; Crossette, N.; Csanád, M.; Csörgő, T.; Dahms, T.; Dairaku, S.; Danchev, I.; Das, K.; Datta, A.; Daugherity, M. S.; David, G.; Dehmelt, K.; Denisov, A.; Deshpande, A.; Desmond, E. J.; Dharmawardane, K. V.; Dietzsch, O.; Ding, L.; Dion, A.; Do, J. H.; Donadelli, M.; D'Orazio, L.; Drapier, O.; Drees, A.; Drees, K. A.; Durham, J. M.; Durum, A.; Dutta, D.; Edwards, S.; Efremenko, Y. V.; Ellinghaus, F.; Engelmore, T.; Enokizono, A.; En'yo, H.; Esumi, S.; Eyser, K. O.; Fadem, B.; Fields, D. E.; Finger, M.; Finger, M.; Fleuret, F.; Fokin, S. L.; Fraenkel, Z.; Frantz, J. E.; Franz, A.; Frawley, A. D.; Fujiwara, K.; Fukao, Y.; Fusayasu, T.; Gainey, K.; Gal, C.; Garg, P.; Garishvili, A.; Garishvili, I.; Giordano, F.; Glenn, A.; Gong, H.; Gong, X.; Gonin, M.; Goto, Y.; Granier de Cassagnac, R.; Grau, N.; Greene, S. V.; Grosse Perdekamp, M.; Gu, Y.; Gunji, T.; Guo, L.; Gustafsson, H.-Å.; Hachiya, T.; Haggerty, J. S.; Hahn, K. I.; Hamagaki, H.; Hamblen, J.; Han, R.; Hanks, J.; Hartouni, E. P.; Hashimoto, K.; Haslum, E.; Hayano, R.; Hayashi, S.; He, X.; Heffner, M.; Hemmick, T. K.; Hester, T.; Hill, J. C.; Hohlmann, M.; Hollis, R. S.; Holzmann, W.; Homma, K.; Hong, B.; Horaguchi, T.; Hori, Y.; Hornback, D.; Huang, S.; Ichihara, T.; Ichimiya, R.; Ide, J.; Iinuma, H.; Ikeda, Y.; Imai, K.; Imazu, Y.; Imrek, J.; Inaba, M.; Iordanova, A.; Isenhower, D.; Ishihara, M.; Isinhue, A.; Isobe, T.; Issah, M.; Isupov, A.; Ivanishchev, D.; Jacak, B. V.; Javani, M.; Jia, J.; Jiang, X.; Jin, J.; Johnson, B. M.; Joo, K. S.; Jouan, D.; Jumper, D. S.; Kajihara, F.; Kametani, S.; Kamihara, N.; Kamin, J.; Kaneti, S.; Kang, B. H.; Kang, J. H.; Kang, J. S.; Kapustinsky, J.; Karatsu, K.; Kasai, M.; Kawall, D.; Kawashima, M.; Kazantsev, A. V.; Kempel, T.; Key, J. A.; Khandai, P. K.; Khanzadeev, A.; Kijima, K. M.; Kim, B. I.; Kim, C.; Kim, D. H.; Kim, D. J.; Kim, E.; Kim, E.-J.; Kim, H. J.; Kim, K.-B.; Kim, S. H.; Kim, Y.-J.; Kim, Y. K.; Kinney, E.; Kiriluk, K.; Kiss, Á.; Kistenev, E.; Klatsky, J.; Kleinjan, D.; Kline, P.; Kochenda, L.; Komatsu, Y.; Komkov, B.; Konno, M.; Koster, J.; Kotchetkov, D.; Kotov, D.; Kozlov, A.; Král, A.; Kravitz, A.; Krizek, F.; Kunde, G. J.; Kurita, K.; Kurosawa, M.; Kwon, Y.; Kyle, G. S.; Lacey, R.; Lai, Y. S.; Lajoie, J. G.; Lebedev, A.; Lee, B.; Lee, D. M.; Lee, J.; Lee, K.; Lee, K. B.; Lee, K. S.; Lee, S. H.; Lee, S. R.; Leitch, M. J.; Leite, M. A. L.; Leitgab, M.; Leitner, E.; Lenzi, B.; Lewis, B.; Li, X.; Liebing, P.; Lim, S. H.; Linden Levy, L. A.; Liška, T.; Litvinenko, A.; Liu, H.; Liu, M. X.; Love, B.; Luechtenborg, R.; Lynch, D.; Maguire, C. F.; Makdisi, Y. I.; Makek, M.; Malakhov, A.; Malik, M. D.; Manion, A.; Manko, V. I.; Mannel, E.; Mao, Y.; Maruyama, T.; Masui, H.; Masumoto, S.; Matathias, F.; McCumber, M.; McGaughey, P. L.; McGlinchey, D.; McKinney, C.; Means, N.; Meles, A.; Mendoza, M.; Meredith, B.; Miake, Y.; Mibe, T.; Midori, J.; Mignerey, A. C.; Mikeš, P.; Miki, K.; Milov, A.; Mishra, D. K.; Mishra, M.; Mitchell, J. T.; Miyachi, Y.; Miyasaka, S.; Mohanty, A. K.; Mohapatra, S.; Moon, H. J.; Morino, Y.; Morreale, A.; Morrison, D. P.; Moskowitz, M.; Motschwiller, S.; Moukhanova, T. V.; Murakami, T.; Murata, J.; Mwai, A.; Nagae, T.; Nagamiya, S.; Nagle, J. L.; Naglis, M.; Nagy, M. I.; Nakagawa, I.; Nakamiya, Y.; Nakamura, K. R.; Nakamura, T.; Nakano, K.; Nattrass, C.; Nederlof, A.; Netrakanti, P. K.; Newby, J.; Nguyen, M.; Nihashi, M.; Niida, T.; Nouicer, R.; Novitzky, N.; Nukariya, A.; Nyanin, A. S.; Obayashi, H.; O'Brien, E.; Oda, S. X.; Ogilvie, C. A.; Oka, M.; Okada, K.; Onuki, Y.; Oskarsson, A.; Ouchida, M.; Ozawa, K.; Pak, R.; Pantuev, V.; Papavassiliou, V.; Park, B. H.; Park, I. H.; Park, J.; Park, S.; Park, S. K.; Park, W. J.; Pate, S. F.; Patel, L.; Pei, H.; Peng, J.-C.; Pereira, H.; Perepelitsa, D. V.; Peresedov, V.; Peressounko, D. Yu.; Petti, R.; Pinkenburg, C.; Pisani, R. P.; Proissl, M.; Purschke, M. L.; Purwar, A. K.; Qu, H.; Rak, J.; Rakotozafindrabe, A.; Ravinovich, I.; Read, K. F.; Reygers, K.; Reynolds, D.; Riabov, V.; Riabov, Y.; Richardson, E.; Riveli, N.; Roach, D.; Roche, G.; Rolnick, S. D.; Rosati, M.; Rosen, C. A.; Rosendahl, S. S. E.; Rosnet, P.; Rukoyatkin, P.; Ružička, P.; Ryu, M. S.; Sahlmueller, B.; Saito, N.; Sakaguchi, T.; Sakashita, K.; Sako, H.; Samsonov, V.; Sano, M.; Sano, S.; Sarsour, M.; Sato, S.; Sato, T.; Sawada, S.; Sedgwick, K.; Seele, J.; Seidl, R.; Semenov, A. Yu.; Sen, A.; Seto, R.; Sett, P.; Sharma, D.; Shein, I.; Shibata, T.-A.; Shigaki, K.; Shimomura, M.; Shoji, K.; Shukla, P.; Sickles, A.; Silva, C. L.; Silvermyr, D.; Silvestre, C.; Sim, K. S.; Singh, B. K.; Singh, C. P.; Singh, V.; Skolnik, M.; Slunečka, M.; Solano, S.; Soltz, R. A.; Sondheim, W. E.; Sorensen, S. P.; Sourikova, I. V.; Sparks, N. A.; Stankus, P. W.; Steinberg, P.; Stenlund, E.; Stepanov, M.; Ster, A.; Stoll, S. P.; Sugitate, T.; Sukhanov, A.; Sun, J.; Sziklai, J.; Takagui, E. M.; Takahara, A.; Taketani, A.; Tanabe, R.; Tanaka, Y.; Taneja, S.; Tanida, K.; Tannenbaum, M. J.; Tarafdar, S.; Taranenko, A.; Tarján, P.; Tennant, E.; Themann, H.; Thomas, T. L.; Todoroki, T.; Togawa, M.; Toia, A.; Tomášek, L.; Tomášek, M.; Torii, H.; Towell, R. S.; Tserruya, I.; Tsuchimoto, Y.; Tsuji, T.; Vale, C.; Valle, H.; van Hecke, H. W.; Vargyas, M.; Vazquez-Zambrano, E.; Veicht, A.; Velkovska, J.; Vértesi, R.; Vinogradov, A. A.; Virius, M.; Voas, B.; Vossen, A.; Vrba, V.; Vznuzdaev, E.; Wang, X. R.; Watanabe, D.; Watanabe, K.; Watanabe, Y.; Watanabe, Y. S.; Wei, F.; Wei, R.; Wessels, J.; Whitaker, S.; White, S. N.; Winter, D.; Wolin, S.; Wood, J. P.; Woody, C. L.; Wright, R. M.; Wysocki, M.; Xia, B.; Xie, W.; Yamaguchi, Y. L.; Yamaura, K.; Yang, R.; Yanovich, A.; Ying, J.; Yokkaichi, S.; You, Z.; Young, G. R.; Younus, I.; Yushmanov, I. E.; Zajc, W. A.; Zelenski, A.; Zhang, C.; Zhou, S.; Zolin, L.; Phenix Collaboration
2016-01-01
We report the measurement of cumulants (Cn,n =1 ,...,4 ) of the net-charge distributions measured within pseudorapidity (|η |distributions, which can be related to volume independent susceptibility ratios, are studied as a function of centrality and energy. These quantities are important to understand the quantum-chromodynamics phase diagram and possible existence of a critical end point. The measured values are very well described by expectation from negative binomial distributions. We do not observe any nonmonotonic behavior in the ratios of the cumulants as a function of collision energy. The measured values of C1/C2 and C3/C1 can be directly compared to lattice quantum-chromodynamics calculations and thus allow extraction of both the chemical freeze-out temperature and the baryon chemical potential at each center-of-mass energy. The extracted baryon chemical potentials are in excellent agreement with a thermal-statistical analysis model.
Stewart, Stan
2004-01-01
Switchgear plays a fundamental role within the power supply industry. It is required to isolate faulty equipment, divide large networks into sections for repair purposes, reconfigure networks in order to restore power supplies and control other equipment.This book begins with the general principles of the Switchgear function and leads on to discuss topics such as interruption techniques, fault level calculations, switching transients and electrical insulation; making this an invaluable reference source. Solutions to practical problems associated with Distribution Switchgear are also included.
Institute of Scientific and Technical Information of China (English)
张茂军; 秦学志; 南江霞
2013-01-01
为了刻画欧式期权价格估计值的不确定性和投资者的犹豫程度,用三角直觉模糊数表示期权标的资产价格的变化因子,构建了三角直觉模糊数二叉树定价模型,并用风险中性定价方法研究单期欧式看涨期权的定价问题.研究发现:欧式看涨期权价格表示为一个三角直觉模糊数,其值体现了投资者对期权价格估计值的肯定程度、否定程度和犹豫程度；利用三角直觉模糊数的截集运算法则得到了欧式看涨期权价格的区间值.数值算例表明,用三角直觉模糊数得到的欧式看涨期权的价格比用三角模糊数得到的价格更能体现投资者的犹豫性.%In this paper the triangular intuitionistic fuzzy numbers are used to express the change factors of the underlying assets of the option in order to describe the uncertainty of the estimated value of the European option price and the hesitation degree of the investors, the intuitionistic fuzzy binomial tree pricing model is made, and the risk neutral pricing method is used to research the single period European call option pricing problem. The findings of the study are that the European option price expressed by a triangular intuitionistic fuzzy number, which can reflect the certainty degree, negation degree and hesitation degree of the investor on the estimated value of the option price, and then the interval value of European option price is obtained by using the cuts sets operation of the triangular intuitionistic fuzzy numbers. Some numerical examples show that European call option price obtained by the triangular intuitionistic fuzzy number can express more the hesitation degree of the investors than the one obtained by the fuzzy number.
DEFF Research Database (Denmark)
Lützen, Marie
2001-01-01
The purpose of Task 2.2 of the HARDER project is according to the work package description: For various structural configurations of the struck ship and using the results of Task 2.1, the probability distributions for the damage location and size will be derived. The format will be similar to the...... damage statistics and bow height statistics for vessels in the world fleet. The proposals for the p-, r-, and v-factors have been compared to factors from current regulation by examples.......The purpose of Task 2.2 of the HARDER project is according to the work package description: For various structural configurations of the struck ship and using the results of Task 2.1, the probability distributions for the damage location and size will be derived. The format will be similar to the p...... between the damage location, the damage sizes and the main particulars of the struck vessel. From the numerical simulation and the analyse of the damage statistics it is found that the current formulation from the IMO SLF 43/3/2 can be used as basis for determination of the p-, r-, and v...
Directory of Open Access Journals (Sweden)
Gómez Déniz, Emilio
2013-01-01
Full Text Available In this paper the analysis of the collective risk model assuming Erlang loss, when the claim frequency follows the discrete generalized Lindley distribution, is considered. After providing some new results of this discrete model, analytical expressions for the aggregate claim size distribution in general insurance in the case that the discrete generalized Lindley distribution is assumed as the primary distribution while claim size, the secondary distribution, is modeled using an Erlang(r distribution (r = 1; 2. Comparisons with the compound Poisson and compound negative binomial are developed to explain the viability of the new compound model in two examples in automobile insurance. || En este artículo se analiza el modelo de riesgo colectivo asumiendo que la cantidad individual reclamada sigue una función de densidad Erlang y el número de reclamaciones es una variable aleatoria cuya función masa de probabilidad es la generalizada discreta Lindley. En la primera parte de este trabajo se presentan nuevas propiedades de esta distribución discreta; seguidamente, se calculan expresiones analíticas para la cantidad total reclamada en seguros generales cuando la distribución primaria es la generalizada discreta Lindley, asumiendo la densidad Erlang(r (r = 1; 2 como distribución secundaria. En la ilustración numérica, el nuevo modelo expuesto en este artículo se compara con los modelos compuestos Poisson y Binomial Negativa en dos ejemplos, en el contexto de seguros de automóviles, para mostrar su efectividad.
Institute of Scientific and Technical Information of China (English)
戴朝寿; 候艳艳
2001-01-01
本文证明了负超几何分布在一定条件下,以负二项分布作为其极限分布,而负二项分布在一定条件下,又趋向于Poisson分布;进而,提出了多维负超几何分布的概念,将上述三种分布之间的关系推广到一般多维情形,证明了n维负超几何分布在一定条件下,以负n+1项分布作为其板限分布,而负n+1项分布在一定条件下,又趋向于n维Poisson分布.
Geographic Distribution of Healthy Resources and Adverse Pregnancy Outcomes.
Young, Christopher; Laurent, Olivier; Chung, Judith H; Wu, Jun
2016-08-01
Objective To determine the risk of gestational diabetes (GDM) and preeclampsia associated with various community resources. Methods An ecological study was performed in Los Angeles and Orange counties in California. Fast food restaurants, supermarkets, grocery stores, gyms, health clubs and green space were identified using Google © Maps Extractor and through the Southern California Association of Government. California Birth Certificate data was used to identify cases of GDM and preeclampsia. Unadjusted and adjusted risk ratios were calculated using negative binomial regression. Results There were 9692 cases of GDM and 6288 cases of preeclampsia corresponding to incidences of 2.5 and 1.4 % respectively. The adjusted risk of GDM was reduced in zip codes with greater concentration of grocery stores [relative risk (RR) 0.95, 95 % confidence interval (CI) 0.92-0.99] and supermarkets (RR 0.94, 95 % CI 0.90-0.98). There were no significant relationships between preeclampsia and the concentration of fast food restaurants, grocery store, supermarkets or the amount of green space. Conclusion The distribution of community resources has a significant association with the risk of developing GDM but not preeclampsia. PMID:26994606
International Nuclear Information System (INIS)
When using parametric empirical Bayes estimation methods for estimating the binomial or Poisson parameter, the validity of the assumed beta or gamma conjugate prior distribution is an important diagnostic consideration. Chi-square goodness-of-fit tests of the beta or gamma prior hypothesis are developed for use when the binomial sample sizes or Poisson exposure times vary. Nine examples illustrate the application of the methods, using real data from such diverse applications as the loss of feedwater flow rates in nuclear power plants, the probability of failure to run on demand and the failure rates of the high pressure coolant injection systems at US commercial boiling water reactors, the probability of failure to run on demand of emergency diesel generators in US commercial nuclear power plants, the rate of failure of aircraft air conditioners, baseball batting averages, the probability of testing positive for toxoplasmosis, and the probability of tumors in rats. The tests are easily applied in practice by means of corresponding Mathematica reg-sign computer programs which are provided
Lee, S. J.; Mekjian, A. Z.
2004-01-01
Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are a, x, z. The relation to these parameters to various physical quantities are discussed. A connection of the parameter a with Fisher's critical exponent τ is developed. Using this grand canonical approach, moments, cumulants and combinants are discussed and a physical interpretation of the combinants are given and their behavior connected to the critical exponent τ. Various physical phenomena such as hierarchical structure, void scaling relations, Koba-Nielson-Olesen or KNO scaling features, clan variables, and branching laws are shown in terms of this general approach. Several of these features which were previously developed in terms of the negative binomial distribution are found to be more general. Both hierarchical structure and void scaling relations depend on the Fisher exponent τ. Applications of our approach to the charged particle multiplicity distribution in jets of L3 and H1 data are given.
International Nuclear Information System (INIS)
Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are a,x,z. The relation to these parameters to various physical quantities are discussed. A connection of the parameter a with Fisher's critical exponent τ is developed. Using this grand canonical approach, moments, cumulants and combinants are discussed and a physical interpretation of the combinants are given and their behavior connected to the critical exponent τ. Various physical phenomena such as hierarchical structure, void scaling relations, Koba-Nielson-Olesen or KNO scaling features, clan variables, and branching laws are shown in terms of this general approach. Several of these features which were previously developed in terms of the negative binomial distribution are found to be more general. Both hierarchical structure and void scaling relations depend on the Fisher exponent τ. Applications of our approach to the charged particle multiplicity distribution in jets of L3 and H1 data are given
Directory of Open Access Journals (Sweden)
Córdova-Izquierdo, Alejandro
2010-05-01
focused on teacher activity and promoting a passive student. The approach above is the proposal to consider the binomial-stress adaptation and animal welfare as axes in the education of veterinarians. In this proposal the autonomic nervous system (ANS isconsidered as a key to explain the reactions of animals to environmental stimuli. The term autonomic nervous system was coined by Langley (early twentieth century, to distinguish the portion of the nervous system, which is not under voluntary control and that functions as an efferent (motor system, to transmit control signals to the whole organism with the exception of striated muscle.
Fitting the distribution of dry and wet spells with alternative probability models
Deni, Sayang Mohd; Jemain, Abdul Aziz
2009-06-01
The development of the rainfall occurrence model is greatly important not only for data-generation purposes, but also in providing informative resources for future advancements in water-related sectors, such as water resource management and the hydrological and agricultural sectors. Various kinds of probability models had been introduced to a sequence of dry (wet) days by previous researchers in the field. Based on the probability models developed previously, the present study is aimed to propose three types of mixture distributions, namely, the mixture of two log series distributions (LSD), the mixture of the log series Poisson distribution (MLPD), and the mixture of the log series and geometric distributions (MLGD), as the alternative probability models to describe the distribution of dry (wet) spells in daily rainfall events. In order to test the performance of the proposed new models with the other nine existing probability models, 54 data sets which had been published by several authors were reanalyzed in this study. Also, the new data sets of daily observations from the six selected rainfall stations in Peninsular Malaysia for the period 1975-2004 were used. In determining the best fitting distribution to describe the observed distribution of dry (wet) spells, a Chi-square goodness-of-fit test was considered. The results revealed that the new method proposed that MLGD and MLPD showed a better fit as more than half of the data sets successfully fitted the distribution of dry and wet spells. However, the existing models, such as the truncated negative binomial and the modified LSD, were also among the successful probability models to represent the sequence of dry (wet) days in daily rainfall occurrence.
Baseline measures for net-proton distributions in high energy heavy-ion collisions
Netrakanti, P. K.; Luo, X. F.; Mishra, D. K.; Mohanty, B.; Mohanty, A.; Xu, N.
2016-03-01
We report a systematic comparison of the recently measured cumulants of the net-proton distributions for 0-5% central Au + Au collisions in the first phase of the Beam Energy Scan (BES) Program at the Relativistic Heavy Collider facility to various kinds of possible baseline measures. These baseline measures correspond to an assumption that the proton and anti-proton distributions follow Poisson statistics, Binomial statistics, obtained from a transport model calculation and from a hadron resonance gas model. The higher order cumulant net-proton data for the center of mass energies (√{sNN}) of 19.6 and 27 GeV are observed to deviate from most of the baseline measures studied. The deviations are predominantly due to the difference in shape of the proton distributions between data and those obtained in the baseline measures. We also present a detailed study on the relevance of the independent production approach as a baseline for comparison with the measurements at various beam energies. Our studies point to the need of either more detailed baseline models for the experimental measurements or a description via QCD calculations in order to extract the exact physics process that leads to deviation of the data from the baselines presented.
Product Distributions for Distributed Optimization. Chapter 1
Bieniawski, Stefan R.; Wolpert, David H.
2004-01-01
With connections to bounded rational game theory, information theory and statistical mechanics, Product Distribution (PD) theory provides a new framework for performing distributed optimization. Furthermore, PD theory extends and formalizes Collective Intelligence, thus connecting distributed optimization to distributed Reinforcement Learning (FU). This paper provides an overview of PD theory and details an algorithm for performing optimization derived from it. The approach is demonstrated on two unconstrained optimization problems, one with discrete variables and one with continuous variables. To highlight the connections between PD theory and distributed FU, the results are compared with those obtained using distributed reinforcement learning inspired optimization approaches. The inter-relationship of the techniques is discussed.
Distributed Computing: An Overview
Directory of Open Access Journals (Sweden)
Md. Firoj Ali
2015-07-01
Full Text Available Decrease in hardware costs and advances in computer networking technologies have led to increased interest in the use of large-scale parallel and distributed computing systems. Distributed computing systems offer the potential for improved performance and resource sharing. In this paper we have made an overview on distributed computing. In this paper we studied the difference between parallel and distributed computing, terminologies used in distributed computing, task allocation in distributed computing and performance parameters in distributed computing system, parallel distributed algorithm models, and advantages of distributed computing and scope of distributed computing.
Protection of Distribution Systems with Distributed Generation
Vassbotten, Kristian
2015-01-01
In recent years the amount of distributed generation(DG) in distribution systems have increased. This poses problems for the traditional protection scheme, with non-directional over-current relays and fuses. When DG is introduced the load flow in distribution systems are often reversed; there is a surplus of power on the radial. Present thesis seeks to determine the most beneficial protection scheme to use in distribution systems with DG. To investigate the impact of different relays and...
Bivariate discrete Linnik distribution
Directory of Open Access Journals (Sweden)
Davis Antony Mundassery
2014-10-01
Full Text Available Christoph and Schreiber (1998a studied the discrete analogue of positive Linnik distribution and obtained its characterizations using survival function. In this paper, we introduce a bivariate form of the discrete Linnik distribution and study its distributional properties. Characterizations of the bivariate distribution are obtained using compounding schemes. Autoregressive processes are developed with marginals follow the bivariate discrete Linnik distribution.
Bivariate discrete Linnik distribution
Davis Antony Mundassery; Jayakumar, K.
2014-01-01
Christoph and Schreiber (1998a) studied the discrete analogue of positive Linnik distribution and obtained its characterizations using survival function. In this paper, we introduce a bivariate form of the discrete Linnik distribution and study its distributional properties. Characterizations of the bivariate distribution are obtained using compounding schemes. Autoregressive processes are developed with marginals follow the bivariate discrete Linnik distribution.
Some properties of compound Poisson-Geometric distribution%关于复合Poisson-Geometric分布的几个性质
Institute of Scientific and Technical Information of China (English)
包振华; 徐海坤; 刘志鹏
2011-01-01
在经典的风险模型中,描述赔付次数的过程是齐次Poisson过程.然而在保险实践中,风险事件与赔付事件有可能不是等价的,所以Poisson-Geometric分布比Poisson分布更为适合用来描述索赔次数的分布.利用随机变量的概率母函数研究复合Poisson-Geometric分布关于卷积的封闭性,并且讨论了复合Poisson-Geomet ric分布与复合Poisson分布以及复合广义负二项分布之间的关系.%In the classical risk models, the homogeneous Poisson process is used to describe the number of claims. However, the risk event and claim event are not equivalent in the practical insurance, Pois-son-Geometric distribution is more appropriate for describing the claim numbers than Poisson distribution. Using the technique of probability generating function, we study the closure property of compound Poisson-Geometric distributions under convolution. We discuss the relationship between the compound Poisson-Geometric distribution and compound Poisson distribution. The relationship between compound generalized negative binomial distribution and compound Poisson-Geometric distribution is also investigated.
Directory of Open Access Journals (Sweden)
Tatiana Rojas Rodrigues
2010-03-01
Full Text Available Distribuição espacial de Aphis gossypii (Glover (Hemiptera, Aphididae e Bemisia tabaci (Gennadius biótipo B (Hemiptera, Aleyrodidae em algodoeiro Bt e não-Bt. O estudo da distribuição espacial de adultos de Bemisia tabaci e de Aphis gossypii nas culturas do algodoeiro Bt e não-Bt é fundamental para a otimização de técnicas de amostragens, além de revelar diferenças de comportamento de espécies não-alvo dessa tecnologia Bt entre as duas cultivares. Nesse sentido, o experimento buscou investigar o padrão da distribuição espacial dessas espécies de insetos no algodoeiro convencional não-Bt e no cultivar Bt. As avaliações ocorreram em dois campos de 5.000 m² cada, nos quais se realizou 14 avaliações com contagem de adultos da mosca-branca e colônias de pulgões. Foram calculados os índices de agregação (razão variância/média, índice de Morisita e Expoente k da Distribuição Binomial Negativa e realizados os testes ajustes das classes numéricas de indivíduos encontradas e esperadas às distribuições teóricas de freqüência (Poisson, Binomial Negativa e Binomial Positiva. Todas as análises mostraram que, em ambas as cultivares, a distribuição espacial de B. tabaci ajustou-se a distribuição binomial negativa durante todo o período analisado, indicando que a cultivar transgênica não influenciou o padrão de distribuição agregada desse inseto. Já com relação às análises para A. gossypii, os índices de agregação apontaram distribuição agregada nas duas cultivares, mas as distribuições de freqüência permitiram concluir a ocorrência de distribuição agregada apenas no algodoeiro convencional, pois não houve nenhum ajuste para os dados na cultivar Bt. Isso indica que o algodão Bt alterou o padrão normal de dispersão dos pulgões no cultivo.The study of spatial distribution of the adults of Bemisia tabaci and the colonies of Aphis gossypii on Bt and non-Bt cotton crop is fundamental for
Mizoguchi, Takuya
2012-01-01
Using the negative binomial distribution (NBD) and the generalized Glauber-Lachs (GGL) formula, we analyze the data on charged multiplicity distributions in the several pseudorapidity intervals |\\eta| < \\eta_c at 0.2 - 7 TeV by UA5 and ALICE Collaborations. We confirm that the KNO scaling holds among the multiplicity distributions with \\eta_c = 0.5 at \\sqrt{s} = 0.2 - 2.36 TeV and estimate the energy dependence of a parameter 1/k in NBD and parameters 1/k and \\gamma (the ratio of the average value of the coherent hadrons to that of the chaotic hadrons) in the GGL formula. Using empirical formulae for the parameters 1/k and \\gamma in the GGL formula, we predict the multiplicity distributions with \\eta_c = 0.5 at 7 and 14 TeV. Data on the second order Bose-Einstein correlations (BEC) at 0.9 and 2.36 TeV by ALICE and CMS Collaborations are also analyzed based on the GGL formula. Predictions for the third order BEC at 0.9 and 2.36 TeV are presented.
Zhao, Zheng-shuai; Zheng, Ya-qiong; Liang, Ji-ye; Han, Zhan-jiang; Li, Zhi-jun
2016-02-01
Spatial distribution pattern of Populus euphratica and P. pruinosa clonal ramets at three sites was studied, including natural mixed forest of P. euphratica and P. pruinosa in Awati County located in the downstream of Yarkant River, natural P. pruinosa forest in Group 16 of Nongyishi in the Tarim River upstream area, and natural P. euphratica forest in Luntai County located in the middle reach of the Tarim River. The clonal ramets of the three sites showed a cluster distribution pattern at eight sampling scales, i.e., 5 mx5 m, 5 mx10 m, 5 mx15 m, 10 mx10 m, 10 mx15 m, 15 mx15 m, 15 mx20 m, and 20 mX20 m. This pattern revealed that the cluster distribution was a basic property in the spatial distribution pattern of P. euphratica and P. pruinosa populations. At 5 mx5 m scale, negative binomial parameter was minimum, while Cassie index, patchiness inex and aggregation strength were maximum for the two ramet populations at the three sites. PMID:27396111
Intermittency via moments and distributions in central O+Cu collisions at 14.6 A·GeV/c
International Nuclear Information System (INIS)
Fluctuations in pseudorapidity distributions of charged particles from central (ZCAL) collisions of 16O+Cu at 14.6 A·GeV/c have been analyzed by Ju Kang using the method of scaled factorial moments as a function of the interval δη an apparent power-law growth of moments with decreasing interval is observed down to δη ∼ 0.1, and the measured slope parameters are found to obey two scaling rules. Previous experience with ET distributions suggested that fluctuations of multiplicity and transverse energy can be well described by Gamma or Negative Binomial Distributions (NBD) and excellent fits to NBD were obtained in all δη bins. The k parameter of the NBD fit was found to increase linearly with the δη interval, which due to the well known property of the NBD under convolution, indicates that the multiplicity distributions in adjacent bins of pseudorapidity δη ∼ 0.1 are largely statistically independent
Variable selection for distribution-free models for longitudinal zero-inflated count responses.
Chen, Tian; Wu, Pan; Tang, Wan; Zhang, Hui; Feng, Changyong; Kowalski, Jeanne; Tu, Xin M
2016-07-20
Zero-inflated count outcomes arise quite often in research and practice. Parametric models such as the zero-inflated Poisson and zero-inflated negative binomial are widely used to model such responses. Like most parametric models, they are quite sensitive to departures from assumed distributions. Recently, new approaches have been proposed to provide distribution-free, or semi-parametric, alternatives. These methods extend the generalized estimating equations to provide robust inference for population mixtures defined by zero-inflated count outcomes. In this paper, we propose methods to extend smoothly clipped absolute deviation (SCAD)-based variable selection methods to these new models. Variable selection has been gaining popularity in modern clinical research studies, as determining differential treatment effects of interventions for different subgroups has become the norm, rather the exception, in the era of patent-centered outcome research. Such moderation analysis in general creates many explanatory variables in regression analysis, and the advantages of SCAD-based methods over their traditional counterparts render them a great choice for addressing this important and timely issues in clinical research. We illustrate the proposed approach with both simulated and real study data. Copyright © 2016 John Wiley & Sons, Ltd. PMID:26844819
Spatial distribution of psychotic disorders in an urban area of France: an ecological study.
Pignon, Baptiste; Schürhoff, Franck; Baudin, Grégoire; Ferchiou, Aziz; Richard, Jean-Romain; Saba, Ghassen; Leboyer, Marion; Kirkbride, James B; Szöke, Andrei
2016-01-01
Previous analyses of neighbourhood variations of non-affective psychotic disorders (NAPD) have focused mainly on incidence. However, prevalence studies provide important insights on factors associated with disease evolution as well as for healthcare resource allocation. This study aimed to investigate the distribution of prevalent NAPD cases in an urban area in France. The number of cases in each neighbourhood was modelled as a function of potential confounders and ecological variables, namely: migrant density, economic deprivation and social fragmentation. This was modelled using statistical models of increasing complexity: frequentist models (using Poisson and negative binomial regressions), and several Bayesian models. For each model, assumptions validity were checked and compared as to how this fitted to the data, in order to test for possible spatial variation in prevalence. Data showed significant overdispersion (invalidating the Poisson regression model) and residual autocorrelation (suggesting the need to use Bayesian models). The best Bayesian model was Leroux's model (i.e. a model with both strong correlation between neighbouring areas and weaker correlation between areas further apart), with economic deprivation as an explanatory variable (OR = 1.13, 95% CI [1.02-1.25]). In comparison with frequentist methods, the Bayesian model showed a better fit. The number of cases showed non-random spatial distribution and was linked to economic deprivation. PMID:27189529