Inference on Reliability of Stress-Strength Model with Peng-Yan Extended Weibull Distributions

Abstract

In this paper we estimate $R=P\{X< Y\}$ when $X$ and $Y$ are independent random variables following the Peng-Yan extended Weibull distribution.
We find maximum likelihood estimator of $R$ and its asymptotic distribution. This asymptotic distribution is used
to construct asymptotic confidence intervals. In the case of equal shape parameters, we derive the exact confidence intervals, too.
A procedure for deriving bootstrap-p confidence intervals is presented. The UMVUE of $R$ and the UMVUE of its variance are derived and also the
Bayes point and interval estimator of $R$ for conjugate priors is obtained. Finally, we perform a simulation study in order to compare these estimators
and provide a real data example.