• Title/Summary/Keyword: quasi-negative-binomial distribution

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ON SOME MODELS LEADING TO QUASI-NEGATIVE-BINOMIAL DISTRIBUTION

  • Bilal, Sheikh;Hassan, Anwar
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.11 no.2
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    • pp.15-29
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    • 2007
  • In this paper, we explore some interesting models of the quasi-negative-binomial distribution based on difference differential equations applicable to theory of microorganisms and the situations like that. Some characterizations based on conditional distributions and damage process have been obtained. Further, the distribution of number of accidents as the quasi-negative-binomial distribution in the light of Irwin's theory of ";proneness-liability"; model has been derived. Finally, the proposed model (QNBD) has been applied to study the Shunting accidents, home injuries, and strikes in industries.

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Extended Quasi-likelihood Estimation in Overdispersed Models

  • Kim, Choong-Rak;Lee, Kee-Won;Chung, Youn-Shik;Park, Kook-Lyeol
    • Journal of the Korean Statistical Society
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    • v.21 no.2
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    • pp.187-200
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    • 1992
  • Samples are often found to be too heterogeneous to be explained by a one-parameter family of models in the sense that the implicit mean-variance relationship in such a family is violated by the data. This phenomenon is often called over-dispersion. The most frequently used method in dealing with over-dispersion is to mix a one-parameter family creating a two parameter marginal mixture family for the data. In this paper, we investigate performance of estimators such as maximum likelihood estimator, method of moment estimator, and maximum quasi-likelihood estimator in negative binomial and beta-binomial distribution. Simulations are done for various mean parameter and dispersion parameter in both distributions, and we conclude that the moment estimators are very superior in the sense of bias and asymptotic relative efficiency.

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Adjustments of dispersion statistics in extended quasi-likelihood models (준우도 함수의 분산치 교정)

  • 김충락;서한손
    • The Korean Journal of Applied Statistics
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    • v.6 no.1
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    • pp.41-52
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    • 1993
  • In this paper we study numerical behavior of the adjustments for the variances of the pearson and deviance type dispersion statistics in two overdispersed mixture models; negative binomial and beta-binomial distribution. They are important families of an extended quasi-likelihood model which is very useful for the joint modelling of mean and dispersion. Comparisons are done for two types of dispersion statistics for various mean and dispersion parameters by simulation studies.

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