A New Generalized Poisson-Lindley Distribution: Applications and Properties

Abstract

A new generalized Poisson Lindley distribution is obtained by compounding Poissondistribution with two parameter generalised Lindley distribution. The new distribution isshown to be unimodal and over dispersed. This distribution has a tendency to accommodate right tail as well as for particular values of parameter the tail tends to zero at a faster rate. Various properties like cumulative distribution function, generating function, Moments etc. are derived. Knowledge about the parameters is obtained through Method of Moments, Maximum Likelihood Method and EM Algorithm. Moreover, an actuarial application in collective risk model is shown by considering the proposed distribution as primary and Exponential and Erlang as secondary distribution. The model is applied to real dataset and found to perform better than competing models.