Estimation of Stress-Strength Reliability for the Generalized Pareto Distribution Based on Progressively Censored Samples

Abstract

This paper deals with the estimation of stress-strength reliability parameter, R = P (Y < X ), based on progressively type II censored samples when stress, strength are two independent generalized Pareto random variables. The maximum likelihood estimators, their asymptotic distributions, asymptotic confidence intervals, bootstrap based confidence intervals and Bayes estimators are derived for R. Using Monte Carlo simulations, the MSE, Bayes risk estimators, credible sets and coverage probabilities are computed and compared.

Reliability Inference for the Multicomponent System Based on Progressively Type II Censored Samples from Generalized Pareto Distributions

“…Lio and Tsai [11] studied δ based on progressive first failure-censoring samples from the Burr-XII distributions. Rezaei et al [12] investigated δ based on progressively censored samples from the GP distributions. Based on our best knowledge, no research working on δ s,k for an MSS system based on progressively type II censored samples is found in literature.…”

“…where α > 0 is the shape parameter and λ > 0 is the scale parameter. The GP distribution with Equations (2) and (3) has been used to investigate δ for a single-component system based on random samples (see Rezaei et al [2]) and progressively type II censored samples (see Rezaei et al [12]). In this study, the reliability of an MSS system is investigated based on the GP distribution defined by Equations (2) and (3).…”

“…It is important to mention thatλ is needed to calculate bothα 1 andα 2 . For this purpose, Equations (12) and (13) are used to transform Equation (11) into the following equation…”

“…Rezaei et al [12] presented the asymptotic distribution ofα 1 ,α 2 ,λ andδ 1,1 based on the progressively type II censored samples. The procedure can be extended to derive an approximate confidence interval of δ s,k .…”

Bayesian and Non-Bayesian Inference for the Generalized Pareto Distribution Based on Progressive Type II Censored Sample

“…By combining maximum likelihood estimation and goodness of fit, Husler et al [2] proposed a new estimator for the generalized Pareto distribution. Rezaei et al [3] derived the maximum likelihood estimators, Bayes estimators and some confidence intervals for stress-strength reliability based on progressive Type II censoring schemes.…”