The Exponentiated Generalized-G Poisson Family of Distributions

In this article we propose and study a new family of distributions which is defined by using the genesis of the truncated Poisson distribution and the exponentiated generalized-G distribution. Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics and their moments, reliability and Shannon entropy are derived. Estimation of the parameters using the method of maximum likelihood is discussed. Although this generalization technique can be used to generalize many other distributions, in this study we present only two special models. The importance and flexibility of the new family is exemplified using real world data.