Certain classes of discrete distributions in modeling risk control operations and establishing a transformation for probability generating functions

Abstract

Stochastic interpretations in risk control operations for the class of discrete distributions corresponding to discrete random variables with values in the set of nonnegative integers and unique mode at the point zero, the class of discrete selfdecomposable distributions and the class of discrete distributions corresponding to integral part models are established by the paper. Moreover, the paper introduces a transformation which converts the probability generating function of an integral part model, based on a discrete random variable with values in the set of nonnegative integers and probability function having a unique mode at the point zero, into the probability generating function of a discrete random variable with values in the set of nonnegative integers and selfdecomposable distribution.