The Versatility Of The Negative Binomial Distribution In Describing Dispersion

Abstract

Probability distributions used to describe dispersion are considered. The negative binomial parameter k is considered as a measure of dispersion. The aim of this paper is to demonstrate analytically the versatility of the negative binomial distribution in describing dispersion. The versatility of the negative binomial distribution is established through rcparameterization, truncation, generalizing. mixing and limiting. The bases for this establishment are index of patchiness and probability generating function. The results are summarized in a conceptual distributional framework.