Geodesic
Inference on reliability of stress-strength model with Peng-Yan extended Weibull distributions
Filomat, Tome 35 (2021) no. 6, p. 1927

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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 are obtained. Finally, we perform a simulation study in order to compare these estimators and provide a real data example.
DOI : 10.2298/FIL2106927J
Classification : 62N05, 62F10, 62F12, 62F15, 62F25, 62F40
Keywords: stress-strength, extended Weibull distribution, maximum likelihood estimator, UMVUE, Bayes estimator, bootstrap confidence intervals 
Milan Jovanović; Bojana Milošević; Marko Obradović; Zoran Vidović. Inference on reliability of stress-strength model with Peng-Yan extended Weibull distributions. Filomat, Tome 35 (2021) no. 6, p. 1927 . doi: 10.2298/FIL2106927J
@article{10_2298_FIL2106927J,
     author = {Milan Jovanovi\'c and Bojana Milo\v{s}evi\'c and Marko Obradovi\'c and Zoran Vidovi\'c},
     title = {Inference on reliability of stress-strength model with {Peng-Yan} extended {Weibull} distributions},
     journal = {Filomat},
     pages = {1927 },
     year = {2021},
     volume = {35},
     number = {6},
     doi = {10.2298/FIL2106927J},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2106927J/}
}
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