Estimation of \(\mathrm{Pr}(Y<X)\) for the two-parameter generalized exponential records. (English) Zbl 1359.62159
Summary: This article considers the maximum likelihood and Bayes estimation of the stress-strength reliability based on two-parameter generalized exponential records. Here, we extend the results of A. Baklizi [Comput. Stat. Data Anal. 52, No. 7, 3468–3473 (2008; Zbl 1452.62722)] to explain a wide variety of real datasets. We also consider the estimation of \(R\) when the same shape parameter is known. The results for exponential distribution can be obtained as a special case with different scale parameters.
MSC:
| 62G30 | Order statistics; empirical distribution functions |
| 62E15 | Exact distribution theory in statistics |
| 62E20 | Asymptotic distribution theory in statistics |
| 62F15 | Bayesian inference |
Keywords:
Bayesian estimation; bootstrap confidence interval; maximum likelihood estimator; Metropolis method; record valuesCitations:
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