A New Count Model Generated from Mixed Poisson Transmuted Exponential Family with an application to Health Care Data

Abstract

In this paper, a new mixed Poisson distribution is introduced. This new distribution is obtained by utilizing mixing process, with Poisson distribution as mixed distribution and Transmuted Exponential distribution as mixing distribution. Some distributional properties like unimodality, moments, over-dispersion, Taylor series expansion of proposed model are studied. Estimation of the parameters using method of moments, method of moments and proportion and maximum likelihood estimation along with data fitting experiment to show its advantage over some existing distribution. Further, an actuarial applications in context of aggregate claim distribution is discussed. Finally, we discuss a count regression model based on proposed distribution and its usefulness over some well established model.