Statistical Inference of Stress-Strength Reliability of Gompertz Distribution under Type II Censoring

Abstract

This paper develops the problem of estimating stress-strength reliability for Gompertz lifetime distribution. First, the maximum likelihood estimation (MLE) and exact and asymptotic confidence intervals for stress-strength reliability are obtained. Then, Bayes estimators under informative and noninformative prior distributions are obtained by using Lindley approximation, Monte Carlo integration, and MCMC. Bayesian credible intervals are constructed under these prior distributions. Also, simulation studies are used to illustrate these inference methods. Finally, a real dataset is analyzed to show the implementation of the proposed methodologies.

Bayesian Estimation of the Stress-Strength Reliability Based on Generalized Order Statistics for Pareto Distribution

“…Ten, many studies were performed on the stress-strength parameter based on diferent distributions and diferent conditions governing random variables. Some of the most recently used distributions include two-parameter bathtubshaped lifetime distribution [2], POLO distribution [3], fnite mixture distributions [4], standard two-sided power distribution [5], Kumaraswamy distribution [6], and Gompertz distribution [7].…”