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

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.