The Discrete Poisson-Amarendra Distribution

Abstract

In this paper, a Poisson mixture of the Amarendra distribution, introduced by Shanker (2016 c), is proposed, and called the, “Poisson-Amarendra distribution”. The first four raw moments (about the origin) and central moments (about the mean) are obtained. The expression for coefficient of variation, skewness and kurtosis are also given. For the estimation of its parameter, the maximum likelihood estimation and the method of moments are discussed. Moreover, the distribution is fitted using maximum likelihood estimate to certain data sets to test its goodness of fit over Poisson, Poisson-Lindley and Poisson-Sujatha distributions. The corresponding fitting are found to be quite satisfactory in almost all data sets.