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The comparative studies on stress-strength reliability for Rayleigh distribution
Journal of the Korean Data & Information Science Society 2018;29:1095-108
Published online July 31, 2018
© 2018 Korean Data and Information Science Society.

Ji Eun Oh1 · Joong Kweon Sohn2

12Department of Statistics, Kyungpook National University
Correspondence to: Professor, Department of Statistics, Kyungpook National University, 80 Daehak-ro, Buk-gu, Daegu 41566, Korea, E-mail:
Received March 29, 2018; Revised April 9, 2018; Accepted April 9, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper deals with the estimation of the stress-strength parameter R = P(Y < X) with three different methods for Rayleigh distribution. We assumed that the stress and strength variables are independent.We derive a maximum likelihood estimator of R and its an asymptotic distribution.We also compute an asymptotic confidence intervals. The bootstrap estimator and confidence intervals are also derived based on maximum likelihood estimator of R. We obtained the Bayes estimator based on inversed gamma priors on scale parameters and its most plausible set for constructing the confidence interval of R which is quiet similar to classical confidence interval unlike the highest posterior density region We compare the performances of three estimators using the mean squared error (MSE) of each estimator.
Keywords : Bayes estimator, bootstrap estimator, maximum likelihood estimator, rayleigh distribution, stress-strength reliability.