Discrete Extension of Poisson Distribution for Overdispersed Count Data: Theory and Applications

Abstract

In this study, a new one-parameter discrete probability distribution is introduced for overdispersed count data based on a combining approach. The important statistical properties can be expressed in closed forms including factorial moments, moment generating function, dispersion index, coefficient of variation, coefficient of skewness, coefficient of kurtosis, value at risk, and tail value at risk. Moreover, four classical parameter estimation methods have been discussed for this new distribution. A simulation study was conducted to evaluate the performance of different estimators based on the biases, mean related-errors, and mean square errors of the estimators. In the end, real data sets from different fields are analyzed to verify the usefulness of the new probability mass function over some notable discrete distributions. It is manifested that the new discrete probability distribution provides an adequate fit than these distributions.

Discrete Exponentiated Generalized Family of Distributions

“…Altun et al [7] obtained a new one parameter called discrete Bilal distribution, they studied its statistical properties and estimated the model parameter by using the ML and moment methods. Eliwa et al [16] constructed new continuous and discrete odd DAL-G family of distributions, and they studied some properties of the special models called the new odd DAL-Weibull and discrete new odd DAL-geometric distributions.…”