AN IMPROVED NEGATIVE BINOMIAL TO APPROXIMATE THE POLYA 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...

An Improved Saddlepoint Approximation Based on the Negative Binomial Distribution for the General Birth Process

Daniels (JAP 1982) gave a saddlepoint approximation to the probabilities of a general birth process. This paper gives an improved approximation which is only slightly more complex than Daniels’ approximation and which has considerably reduced relative error in most cases. The new approximation has the characteristic that it is exact whenever the birth rates can be reordered into a linear increa...

On Hypergeometric Generalized Negative Binomial Distribution

An Alternative to the Beta-Binomial Distribution with Application in Developmental Toxicology

The beta-binomial distribution is resulted when the probability of success per trial in the binomial distribution varies in successive trials and the mixing distribution is from the beta family. For experiments with binary outcomes, often it may happen that observations exhibit some extra binomial variation and occur in clusters. In such experiments the beta-binomial distribution can generally ...

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...