Open Access Journal of Biostatistics and Biometrics

The Discrete Poisson-Shanker Distribution

Published on: 2018-07-27

Abstract

In this paper, Poisson-Shanker distribution (PSD) has been obtained by compounding Poisson distribution with Shanker distribution introduced by Shanker [1]. The first four moments about origin and the moments about mean have been obtained. The expressions for coefficients of variation, skewness and kurtosis have been obtained. Mathematical and statistical properties of the PSD including increasing hazard rate, unimodality, over-dispersion, and generating function have been discussed. The estimation of its parameter has been discussed using the method of maximum likelihood and the method of moments. The distribution has been fitted to some data sets to test its goodness of fit over Poisson distribution and Poisson-Lindley distribution (PLD) introduced by Sankaran [2].

Keywords

Shanker Distribution; Compounding; Moments; Statistical Properties; Estimation of Parameters; Goodness of Fit