The Poisson-Transmuted Janardan Distribution for Modelling Count Data

Abstract

In this paper, we introduce a new mixed Poisson distribution, called the Poisson-transmuted Janardan distribution. The Poisson-Janardan and Poisson-Lindley distributions are sub-model of the proposed distribution. Some mathematical properties of the proposed distribution, including the moments, moment generating function, probability generating function and generation of a Poisson-transmuted Janardan random variable, are presented. The parameter estimation is discussed based on the method of moments and the maximum likelihood estimation. In addition, we illustrated the application of the proposed distribution by fitting with 4 real data sets and comparing it with some other distributions based on the Kolmogorov-Smirnov test for criteria.