A New Three-Parameter Mixed Poisson Transmuted Weighted Exponential Distribution with Applications to Insurance Data

Abstract

The classical Poisson distribution assumes equidispersion and this is hardly the case when given count observations. To improve efficiency and general applicability for dispersed data, this paper obtains a new mixing probability distribution using quadratic transmutation map on the weighed exponential distribution. The mixing distribution is used to obtain a new three parameter mixed Poisson distribution. The new distribution has unimodal shape with positive skewness and tends to zero speedily. Basic properties of the new distribution like the distribution function, moments, and dispersion index are obtained. Maximum likelihood estimates of the parameters of the distribution are obtained. Applications are made using four claims frequencies from different insurance companies. Results show that the new distribution gives a good fit in comparisons with some referred discrete distributions.