Estimation of Pr( X < Y) for exponential power records

In this study, we tackle the problem of estimation of stress-strength reliability R = Pr( 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.

Automated summary

This study addresses the estimation problem of stress-strength reliability R = Pr( X < Y) based on upper record values for exponential power distribution. We employ maximum likelihood and Bayes methods to estimate R. The Tierney-Kadane approximation is used for the Bayes estimation of R due to the lack of analytical solution. Asymptotic confidence interval is derived based on the asymptotic distribution of the maximum likelihood estimator of R. A Monte Carlo simulation study is conducted to compare the performances of maximum likelihood estimators and Bayes estimators using mean square error criteria. Finally, a real data application is presented.