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

TL;DR

This paper introduces a new mixed Poisson distribution derived from the Transmuted Exponential family, with applications in healthcare data and count regression modeling, demonstrating its advantages over existing models.

Contribution

A novel mixed Poisson distribution based on the Transmuted Exponential family, with detailed properties, estimation methods, and practical applications in healthcare and actuarial science.

Findings

The new distribution exhibits over-dispersion and unimodality.

Parameter estimation methods are effectively applied to real data.

The proposed count regression model outperforms established models.

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.