THE NEGATIVE BINOMIAL DISTRIBUTION

The Weibull Negative Binomial Distribution

We propose the Weibull negative binomial distribution that is a quite flexible model to analyze positive data, and includes as special submodels the Weibull, Weibull Poisson and Weibull geometric distributions. Some of its structural properties follow from the fact that its density function can be expressed as a mixture of Weibull densities. We provide explicit expressions for moments, generati...

On Hypergeometric Generalized Negative Binomial Distribution

Negative Binomial-Lindley Distribution and Its Application

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...

Quasi-negative binomial distribution: Properties and applications

In this paper, a quasi-negative binomial distribution (QNBD) derived from the class of generalized Lagrangian probability distributions is studied. The negative binomial distribution is a special case of QNBD. Some properties of QNBD, including the upper tail behavior and limiting distributions, are investigated. It is shown that the moments do not exist in some situations and the limiting dist...

The Negative Binomial Distribution Efficiency in Finite Mixture of Semi-parametric Generalized Linear Models

Introduction Selection the appropriate statistical model for the response variable is one of the most important problem in the finite mixture of generalized linear models. One of the distributions which it has a problem in a finite mixture of semi-parametric generalized statistical models, is the Poisson distribution. In this paper, to overcome over dispersion and computational burden, finite ...