共查询到20条相似文献,搜索用时 31 毫秒
1.
S. R. Paul 《统计学通讯:理论与方法》2013,42(6):1497-1506
A new three-parameter distribution, a generalization of the binomial, th ebeta-binomial (BB) and the correlated binomial (CB) distributions, is derived. Improvement in fit of the new distribution over the BB and the CB distributions has been found for a set of real data 相似文献
2.
S.H. Ong 《统计学通讯:理论与方法》2013,42(4):1303-1322
This paper considers further mixture formulations of the bivariate negative binomial (BNB) distribution of Edwards and Gurland (1961) and Subrahmaniam (1966). These formulations and some known ones are applied (1) to obtain a bivariate generalized negative binomial (BGNB) distribution of Bhattacharya (1966), (2) to establish a connection between the accident-proneness models given by the BNB, BGNB and Bhattacharya's bivariate distributions, and (3) to compute the grade correlation and distribution function of the Wicksell-Kibble bivariate gamma distribution. 相似文献
3.
This paper presents a new departure in the generalization of the binomial distribution by adopting the assumption that the underlying Bernoulli trials take on the values α or β where α < β, rather than the conventional values 0 or 1. The adoption of this more general assumption renders the binomial distribution a four-parameter distribution of the form B(n,p,α,β), and requires the generalization of Romanovsky's (1923) reduction formula for central moments. This paper assesses the usefulness of B(n,p,α,β), and its reduction formula, in the numerical analysis of two problems of interest to decision theorists. 相似文献
4.
Zhaoliang Wang 《Journal of statistical planning and inference》2011,141(3):1153-1160
In this paper we do some research on a three-parameter distribution which is called beta-negative binomial (BNB) distribution, a beta mixture of negative binomial (NB) distribution. The closed form and the factorial moment of the BNB distribution are derived. In addition, we present the recursion on the pdf of BNB stopped-sum distribution, and make stochastic comparison between BNB and NB distributions. Furthermore, we have shown that BNB distribution has heavier tail than NB distribution. The application of BNB distribution is carried out on one sample of insurance data. Based on the results, we have shown that the BNB provides a better fit compared to the Poisson and the NB for count data. 相似文献
5.
《Journal of Statistical Computation and Simulation》2012,82(3):524-534
Negative binomial group distribution was proposed in the literature which was motivated by inverse sampling when considering group inspection: products are inspected group by group, and the number of non-conforming items of a group is recorded only until the inspection of the whole group is finished. The non-conforming probability p of the population is thus the parameter of interest. In this paper, the confidence interval construction for this parameter is investigated. The common normal approximation and exact method are applied. To overcome the drawbacks of these commonly used methods, a composite method that is based on the confidence intervals of the negative binomial distribution is proposed, which benefits from the relationship between negative binomial distribution and negative binomial group distribution. Simulation studies are carried out to examine the performances of our methods. A real data example is also presented to illustrate the application of our method. 相似文献
6.
B.K. Ghosh 《统计学通讯:理论与方法》2013,42(4):427-438
Two new normal approximations are proposed for the cumulative binomial distribution when the mean-is reasonably large. Their adequacy is compared with that of certain well-known approximations- The first is recommended for its simplicity and accuracy relative to the standard and Gram-Charlier approximations. The second Is shown to be more accurate than all known approximations for a certain range of the probability of success. 相似文献
7.
Joseph J. Walker 《统计学通讯:模拟与计算》2013,42(4):515-519
Several alternatives to the most common approximation to the inverse moments of the positive binomial distribution are obtained. The method is based on equating moments and gives considerably better approximations for some values of the parameters. 相似文献
8.
J. Rodríguez-Avi A. Conde-Sánchez A. J. Sáez-Castillo M. J. Olmo-Jiménez 《Journal of the Royal Statistical Society. Series C, Applied statistics》2007,56(1):51-61
Summary. The paper describes a distribution generated by the Gaussian hypergeometric function that may be seen as a generalization of the beta–binomial distribution. It is expressed as a generalized beta mixture of a binomial distribution. This new mixing distribution allows the existence of a mode and an antimode, which is very useful for fitting some data sets. Two examples illustrate the greater versatility of the new distribution compared with the beta–binomial distribution. 相似文献
9.
Takemi Yanagimoto 《统计学通讯:理论与方法》2013,42(10):3625-3633
A particular case of Jain and Consul's (1971) generalized neg-ative binomial distribution is studied. The name inverse binomial is suggested because of its close relation with the inverse Gaussian distribution. We develop statistical properties including conditional inference of a parameter. An application using real data is given. 相似文献
10.
11.
In this note, we derive the exact distribution of S by using the method of generating function and BELL polynomials, where S = X1 + X2 + ??? + Xn, and each Xi follows the negative binomial distribution with arbitrary parameters. As a particular case, we also obtain the exact distribution of the convolution of geometric random variables. 相似文献
12.
Byung Soo Kim 《统计学通讯:理论与方法》2013,42(11):3733-3741
In t h i s note mixture models are used to represent overdispersion relative to Poisson or binomial distributions. We flnd a sufflclent condition on the mixing distribution underich the detection of mixture departures from the Poisson or binomial adrnits a locally most powerful unbiased test. The conditions specify plynoria: relations between the variance and mean of Le glxing distribution. 相似文献
13.
《Journal of Statistical Computation and Simulation》2012,82(1-2):33-39
The maximum likelihood estimation of parameters of the Poisson binomial distribution, based on a sample with exact and grouped observations, is considered by applying the EM algorithm (Dempster et al, 1977). The results of Louis (1982) are used in obtaining the observed information matrix and accelerating the convergence of the EM algorithm substantially. The maximum likelihood estimation from samples consisting entirely of complete (Sprott, 1958) or grouped observations are treated as special cases of the estimation problem mentioned above. A brief account is given for the implementation of the EM algorithm when the sampling distribution is the Neyman Type A since the latter is a limiting form of the Poisson binomial. Numerical examples based on real data are included. 相似文献
14.
Diego I. Gallardo Yolanda M. Gómez Mário de Castro 《Journal of Statistical Computation and Simulation》2017,87(12):2291-2297
In this note we present a modification in the EM algorithm for the destructive negative binomial cure rate model. This alteration enables us to obtain the estimates of the whole parameter vector from the complete log-likelihood function, avoiding the corresponding observed log-likelihood function, which is more involved. To achieve this goal, we resort to the mixture representation of the negative binomial distribution in terms of the Poisson and gamma distributions. 相似文献
15.
16.
Konstantinos Adamidis 《Australian & New Zealand Journal of Statistics》1999,41(2):213-221
An EM algorithm is proposed for computing estimates of parameters of the negative bi-nomial distribution; the algorithm does not involve further iterations in the M-step, in contrast with the one given in Schader & Schmid (1985). The approach can be applied to the corresponding problem in the logarithmic series distribution. The convergence of the proposed scheme is investigated by simulation, the observed Fisher information is derivedand numerical examples based on real data are presented. 相似文献
17.
Michael Weba 《Statistical Papers》2002,43(3):445-452
n possibly different success probabilities p
1, p
2, ..., p
n
is frequently approximated by a Poisson distribution with parameter λ = p
1 + p
2 + ... + p
n
. LeCam's bound p
2
1 + p
2
2 + ... + p
n
2 for the total variation distance between both distributions is particularly useful provided the success probabilities are
small.
The paper presents an improved version of LeCam's bound if a generalized d-dimensional Poisson binomial distribution is to be approximated by a compound Poisson distribution.
Received: May 10, 2000; revised version: January 15, 2001 相似文献
18.
P. C. Consul 《统计学通讯:理论与方法》2013,42(2):673-690
The generalized negative binomial (GNB) distribution was defined by Jain and Consul (SIAM J. Appl. Math., 21 (1971)) and was obtained as a particular family of Lagrangian distributions by Consul and Shenton (SIAM J. Appl. Math., 23 (1973)). Consul and Shenton also gave the probability generating function (p.g.f.) and proved many properties of the GNBD. Consul and Gupta (SIAM J. Appl. Math., 39 (1980)) proved that the parameter β must be either zero or 1≤ β ≤ θ-1 for the GNBD to be a true probability distribution and proved some other properties. Numerous applications and properties of this model have been studied by various researchers. Considering two independent GNB variates X and Y, with parameters (m,β,θ) and (n,β,θ) respectively, the probability distribuition of D = Y-X and its p.g.f. and cumulant generating function have been obtained. A recurrence relation between the cumulants has been established and the first four cumulants, β1 and β2 have been derived. Also some moments of the absolute difference |Y-X| have been obtained. 相似文献
19.
《Journal of Statistical Computation and Simulation》2012,82(5):1013-1025
The negative binomial (NB) is frequently used to model overdispersed Poisson count data. To study the effect of a continuous covariate of interest in an NB model, a flexible procedure is used to model the covariate effect by fixed-knot cubic basis-splines or B-splines with a second-order difference penalty on the adjacent B-spline coefficients to avoid undersmoothing. A penalized likelihood is used to estimate parameters of the model. A penalized likelihood ratio test statistic is constructed for the null hypothesis of the linearity of the continuous covariate effect. When the number of knots is fixed, its limiting null distribution is the distribution of a linear combination of independent chi-squared random variables, each with one degree of freedom. The smoothing parameter value is determined by setting a specified value equal to the asymptotic expectation of the test statistic under the null hypothesis. The power performance of the proposed test is studied with simulation experiments. 相似文献
20.
Hubert J. Chen 《统计学通讯:理论与方法》2013,42(21):2707-2712
Sample size determination for testing the hypothesis of equality of proportions with a specified type I and type I1 error probabilitiesis of ten based on normal approximation to the binomial distribution. When the proportionsinvolved are very small, the exact distribution of the test statistic may not follow the assumed distribution. Consequently, the sample size determined by the test statistic may not result in the sespecifiederror probabilities. In this paper the author proposes a square root formula and compares it with several existing sample size approximation methods. It is found that with small proportion (p≦.01) the squar eroot formula provides the closest approximation to the exact sample sizes which attain a specified type I and type II error probabilities. Thes quare root formula is simple inform and has the advantage that equal differencesare equally detectable. 相似文献