Another Generalization of the Geometric Distribution

Abstract

This paper examines a novel extension of the geometric distribution characterized by two parameters, that is not created based on discretizing existing continuous models. This model, due to its analytical form of the cumulative distribution function and simple structure, can be of interest from mathematical perspectives, particularly in cases where the analysis of stochastic orders is desired. In addition, it is a suitable candidate for analyzing monotone hazard rate discrete data, in view of the fact that its hazard rate function exhibits monotonicity in both increasing and decreasing directions. Additionally, the behavior of the survival function of residual lifetime is briefly addressed. The parameters of the distribution are estimated using the maximum likelihood method, and a real-world data set is scrutinized to assess the distribution's adequacy in providing satisfactory fits. © (2024), (Iranian Statistical Society). All rights reserved.