ZERO-INFLATED POISSON TRANSMUTED WEIGHTED EXPONENTIAL DISTRIBUTION: PROPERTIES AND APPLICATIONS

Abstract

Count observations with high frequencies of zero counts abound in diverse fields. In actuary science, for example, insurance claims are often underreported, leading to a higher frequency of zero counts. This invariably reduces the mean and leads to over-dispersion. Different techniques to model such occurrences exist. This study uses the cubic rank transmutation map to compound the weighted exponential distribution and obtain a new count distribution in the mixed Poisson paradigm. The zero-inflated form of the proposition is obtained along with some mathematical properties. Simulated skewness, kurtosis, and dispersion index for the new distributions reveal they are suitable for model dispersed observation with positive skewness. Five datasets with high frequencies of zero counts are used to assess the performance of the new distribution along with some popular count distributions by using the maximum likelihood for parameter estimation. Results show that the natural form of the new proposition performs creditably better than its zero-inflated forms, even when there is a higher proportion of zero counts. The classical negative binomial distribution is also observed to outperform its zero-inflated form in most cases. In contrast, the zero-inflated Poisson distribution better fits the datasets than the classical Poisson distribution.