A generalized inverse trinomial distribution with application

Abstract

This paper considers a particular generalized inverse trinomial distribution which may be regarded as the convolution of binomial and negative distributions for the statistical analysis of count data. This distribution has the flexibility to cater for under-, equi- and over-dispersion in the data. Some basic and probabilistic properties and tail approximation of the distribution have been derived. Conditions for the numerical stability of the two-term probability recurrence formula have also been examined to facilitate computation. For the purpose of statistical analysis, test of hypothesis for equi-dispersion by the score and likelihood ratio tests and simulation study of their power, parameter estimation by maximum likelihood and a probability generating function based methods have been considered. The versatility of the distribution is illustrated by its application to real biological data sets which exhibit under and over dispersion. It is shown that the distribution fits better than the well-known generalized Poisson and COM-Poisson distributions.