Estimation of stress-strength reliability for generalized Gompertz distribution under progressive type-II censoring

Abstract

In this study, the stress-strength reliability, R = P(Y < X) where Y represents the stress of a component and X represents this component’s strength, is obtained when X and Y have two independents generalized Gompertz distribution with different shape parameters under progressive type-II censoring. The Bayes and maximum likelihood estimators of stress-strength reliability can not be acquired in closed forms. The approximate Bayes estimators under squared error loss function by using Lindley’s approximations for stressstrength reliability are derived. A Monte Carlo simulation study is done to check performances of the approximate Bayes against performances of maximum likelihood estimators and observe the coverage probabilities and the intervals’ average width. In addition, the coverage probabilities of the parametric bootstrap estimates are calculated. Two applications based on real datasets are provided.

Bayes Estimation for the Rayleigh–Weibull Distribution Based on Progressive Type-II Censored Samples for Cancer Data in Medicine

“…There are a lot of studies that refer to the parameter estimation of different distributions under PTR-II censored samples (Ali Mousa [17], Balakrishnan [18], Ali Mousa and Al-Sagheer [19], Wu et al [20], Panahi and Asadi [21], Aljuaid [22], Ahmed [23], Singh et al [24], Liao ang Gui [25], Abbas et al [26], Sultan et al [27], Alshenawy [28], Mukhtar [29], Wu and Gui [30], Almongy et al [31], Qiao and Gui [32], Wu [33], El-Morshedy et al [34], El-Sherpieny et al [35], Liang et al [36], Alshenawy et al [37], Almetwally et al [38], Muhammed and Almetwally [39], Çiftci et al [40]). Based on the above studies, the main purpose of this study is to obtain the approximate Bayes estimators under the square error loss functions and then to check them with maximum likelihood estimators (MLEs) in the aspect of the estimated risk (ER).…”