Modified Partial-Geometric Distribution: Properties, Method of Estimations and Numerical Simulation

Abstract

This article introduces a modified version of the partial-geometric distribution, derived by raising the partial-geometric cumulative distribution function to the power of a positive real number. Several distributional functions and quantities of the proposed distributions are derived. A significant property of the proposed distribution, other than exhibiting various dispersal behaviors, is its non-constant hazard rate function, a characteristic not present in the original partial-geometric distribution. Several estimation methods for the model parameters are discussed. However, maximum likelihood estimation (MLE) is ultimately employed due to its simplicity and unbiasedness. Numerical studies are conducted to examine the quality of MLE estimators, demonstrating that the average estimate for each parameter tends its true value as the sample size gets larger.