Caner TANIŞ, Buğra SARAÇOĞLU, Akbar ASGHARZADEH, Mousa ABDİ

Estimation of $Pr(X

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

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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