Poisson-Beta Exponential Distribution: Properties and Applications

Abstract

A new generalized version of the mixed Poisson distribution, called the Poisson-beta exponential (PBE) distribution, is obtained by mixing the Poisson and the beta exponential (BE) distributions. Estimation of the parameters, using the method of moments and maximum likelihood estimators, is discussed. We show the consistency of the new model parameters using simulation study. Examples are given for fitting the PBE distribution to data, and the fit model is compared with that obtained using other distributions.