A quasi Poisson-Akash distribution and its applications to ecology

Abstract

In this paper, a quasi-Poisson-Akash distribution (QPAD) of which Poisson-Akash distribution (PAD) of Shanker (2017 a) is a particular case, has been proposed by compounding Poisson distribution with quasi Akash distribution (QAD), introduced by Shanker (2015). The raw moments and central moments have been obtained. Expressions for coefficient of variation, skewness, kurtosis and index of dispersion have been given their behaviors have been studied for varying values of the parameters. The QPAD has been shown to be unimodal and always over-dispersed. The estimation of its parameters has been discussed using both the method of moments and the method of maximum likelihood. Finally, the goodness of fit of QPAD has been discussed with two real count datasets from ecology and the fit has been compared with that of Poisson distribution (PD), Poisson-Lindley distribution (PLD) and Poisson-Akash distribution (PAD).