A New Generalized Poisson-Lindley Distribution: Applications and Properties

A new generalized Poisson-Lindley distribution is obtained by compounding Poisson distribution with a two parameter generalised Lindley distribution. The new distribution is shown to be unimodal and over-dispersed. This distribution has a tendency to accommodate right tail, and 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 to collective risk model is shown by considering the proposed distribution as primary distribution and exponential and Erlang as secondary distributions. The model is applied to real data sets and found to perform better than other competing models.