Estimation of $Pr(X
Authors : Caner TANIŞ, Buğra SARAÇOĞLU, Akbar ASGHARZADEH, Mousa ABDİ
Pages : 499-511
Doi:10.15672/hujms.847176
View : 25 | Download : 11
Publication Date : 2023-03-31
Article Type : Research Paper
Abstract :In this study, we tackle the problem of estimation of stress-strength reliability $R = P rinsert ignore into journalissuearticles values(X < Y );$ based on upper record values for exponential power distribution. We use the maximum likelihood and Bayes methods to estimate R. The Tierney-Kadane approximation is used to compute the Bayes estimation of R since the Bayes estimator can not be obtained analytically. We also derive asymptotic confidence interval based on the asymptotic distribution of the maximum likelihood estimator of R. We consider a Monte Carlo simulation study in order to compare the performances of the maximum likelihood estimators and Bayes estimators according to mean square error criteria. Finally, a real data application is presented.
Keywords : Upper record values, maximum likelihood estimator, Bayesian estimation, asymptotic confidence interval, Tierney Kadane approximation
Authors : Caner TANIŞ, Buğra SARAÇOĞLU, Akbar ASGHARZADEH, Mousa ABDİ
Pages : 499-511
Doi:10.15672/hujms.847176
View : 25 | Download : 11
Publication Date : 2023-03-31
Article Type : Research Paper
Abstract :In this study, we tackle the problem of estimation of stress-strength reliability $R = P rinsert ignore into journalissuearticles values(X < Y );$ based on upper record values for exponential power distribution. We use the maximum likelihood and Bayes methods to estimate R. The Tierney-Kadane approximation is used to compute the Bayes estimation of R since the Bayes estimator can not be obtained analytically. We also derive asymptotic confidence interval based on the asymptotic distribution of the maximum likelihood estimator of R. We consider a Monte Carlo simulation study in order to compare the performances of the maximum likelihood estimators and Bayes estimators according to mean square error criteria. Finally, a real data application is presented.Keywords : Upper record values, maximum likelihood estimator, Bayesian estimation, asymptotic confidence interval, Tierney Kadane approximation