Analysis of skewed data by using compound Poisson exponential distribution with applications to insurance claims

Abstract

The main aim of this paper is to introduce a new family of distributions, namely compound zero-truncated Poisson exponential distribution of which exponential distribution is a special case. The proposed family of distributions represents the zero truncated-Poisson sum of independent and identically distributed exponential random variables. The proposed distribution has two parameters and its probability density function can be skewed and unimodal. It can be used quite effectively in analyzing skewed data. We suggest to use expectation–maximization (EM)-type algorithm to estimate the unknown parameters, and it is observed that it is easy to implement in practice. We further consider the bivariate version of the proposed model which has three parameters and provides different properties. We have performed extensive simulation studies to see the performances of the proposed EM algorithm, and a real data set has been analyzed to see the effectiveness of the proposed models.