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

Year 2023, Volume: 52 Issue: 2, 499 - 511, 31.03.2023

Caner Tanış , Buğra Saraçoğlu , Akbar Asgharzadeh , Mousa Abdi

https://doi.org/10.15672/hujms.847176

Cited By: 4

https://izlik.org/JA95AN86NW

Abstract

In this study, we tackle the problem of estimation of stress-strength reliability $R = P r(X < Y )$ 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

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