Estimation of Pr(Y < X) for the two-parameter generalized exponential records

ABSTRACT

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 Baklizi [Computational Statistics and Data Analysis 52 (2008), 3468–3473] 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.

Keywords:

• Bayesian estimation
• Bootstrap confidence interval
• Maximum likelihood estimator
• Metropolis method
• Record values

Mathematics Subject Classification:

• 62G30
• 62E15
• 62E20
• 62F15

Acknowledgments

The authors would like to thank the referees for their valuable comments in revising the article. The third author would like to thank the University of Jordan for supporting this research work.