Application of the Geometric Distribution in Stress–Strength Reliability Analysis:A Comparative Study between Maximum Likelihood Estimation and Bayesian Estimation under Kumaraswamy Prior Distribution and Exponential Loss Function

Abstract

In this study, the stress–strength reliability of the geometric distribution was estimated. Two estimation methods were employed: the Bayesian method under an exponential loss function, using the Kumaraswamy prior distribution with hyper parameters
a=(0.3,0.9)a = (0.3, 0.9)a=(0.3,0.9) and b=(3,3.5)b = (3, 3.5)b=(3,3.5), and the Maximum Likelihood Estimation (MLE) method.

Monte Carlo simulation was used to obtain the estimators. One of the most important conclusions reached was the superior efficiency of the Bayesian method under the exponential loss function, particularly in the presence of the hyper parameters (a,b)=(0.3,3).