A new flexible discrete distribution with applications to count data

In this paper we have explored a new discrete probability mass function that has been generated through compounding mechanism. This newly proposed probability mass function is essentially a mixture of Poisson and Ailamujia distribution. Furthermore the parameter estimation has also been discussed by using Maximum likelihood estimation (MLE) technique. Moreover, we have also studied some important properties of the proposed model that include factorial moments, raw moments, mean, variance, and coefficient of variation. In the end, the application and potentiality of the proposed model have been tested statistically and it has been shown that the proposed model can be employed to model a real life data set to get an adequate fit that has also corroborated through graphically. © 2020 The Authors. Published by Atlantis Press SARL. This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).