A Generalized Composite Power Series Family of Distributions with Application to Real Data

Abstract

In this article, we introduce a new flexible family of discrete probability distributions called the generalized composite power series (GCPS). This family was constructed by combining two classes of discrete distributions to generate a wide range of flexible discrete probability models. We derived the probability mass functions and cumulative distribution function used to characterize members of the GCPS family. To demonstrate its flexibility, we herein present two specific members: the generalized geometric zero-truncated Poisson (GGZTP) and the generalized geometric logarithmic (GGL) distributions. Various statistical properties of the GGZTP and GGL distributions are explored, and parameter estimation methods are discussed. To showcase their potential as alternative discrete distributions for count data, we demonstrate their applicability to real datasets, along with a comparative analysis involving two well-known flexible discrete distributions.