期刊名称：Journal of Modern Applied Statistical Methods
出版年度：2016
卷号：15
期号：1
页码：25
出版社：Wayne State University
摘要：Our interest is in estimating the stress-strength reliability R = P[Y < X], where X and Y follow the Lomax distribution with common scale parameter. We discuss the problem in the situation where the stress measurements and the strength measurements are both in terms of records. Firstly, we obtain the MLE of R in general case (the common scale parameter is unknown). The MLE of the three unknown parameters can be obtained by solving one non-linear equation. We provide a simple fixed point type algorithm to find the MLE. We propose percentile bootstrap confidence intervals of R. A Bayes point estimator of R, and the corresponding credible interval using the MCMC sampling technique have been proposed. Secondly, assuming the common scale parameter is known, the MLE of R is obtained. Using exact distributions of the MLEs of the two unknown parameters, we construct the exact confidence interval of R. In this case, Bayes estimators have been obtained using Lindley's approximations. Analysis of a simulated data set has been presented for illustrative purposes. Finally, the different proposed methods have been compared via Monte Carlo simulation study.
关键词：Stress-strength model; Lomax distribution; Maximum likelihood estimation; Bootstrap confidence intervals; credible intervals; Gibbs sampling; Markov Chain Monte Carlo.
