Some contributions to inflated generalized power series distributions

Abstract

The family of generalized power series (GPS) distributions contains some known discrete distributions whose zero-inflated and inflated-parameter extensions have been used to model different types of dependent counts in various fields such as insurance, finance, biometrics, etc. However, in such extensions, the inflated parameter has been considered to be a constant value. In this paper, we shall first compare such extended distributions for the Bernoulli case with its mixture, when the inflated parameter is a random variable, in various types of stochastic orderings. Then, we shall investigate modality and divisibility properties of known members of inflated-parameter GPS distributions. Our findings happen to be the same as those for the classic GPS distributions except for the Bernoulli's case. © 2011 Pakistan Journal of Statistics.