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Estimation of the stress-strength reliability for the generalized logistic distribution. (English) Zbl 07035617
Summary: A. Ragab [“Estimation and predictive density for the generalized logistic distribution”, Microelectron. Reliab. 31, No. 1, 91–95 (1991; doi:10.1016/0026-2714(91)90353-9)] described the Bayesian and empirical Bayesian methods for estimation of the stress-strength parameter \(R = P(Y < X)\), when \(X\) and \(Y\) are independent random variables from two generalized logistic (GL) distributions having the same known scale but different shape parameters. In this current paper, we consider the estimation of \(R\), when \(X\) and \(Y\) are both two-parameter GL distribution with the same unknown scale but different shape parameters or with the same unknown shape but different scale parameters. We also consider the general case when the shape and scale parameters are different. The maximum likelihood estimator of \(R\) and its asymptotic distribution are obtained and it is used to construct the asymptotic confidence interval of \(R\). We also implement Gibbs and Metropolis samplings to provide a sample-based estimate of \(R\) and its associated credible interval. Finally, analyzes of real data set and Monte Carlo simulation are presented for illustrative purposes.

MSC:
62-XX Statistics
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