ABSTRACT
In this article, we consider the problem of estimation of the stress–strength parameter δ = P(Y < X) based on progressively first-failure-censored samples, when X and Y both follow two-parameter generalized inverted exponential distribution with different and unknown shape and scale parameters. The maximum likelihood estimator of δ and its asymptotic confidence interval based on observed Fisher information are constructed. Two parametric bootstrap boot-p and boot-t confidence intervals are proposed. We also apply Markov Chain Monte Carlo techniques to carry out Bayes estimation procedures. Bayes estimate under squared error loss function and the HPD credible interval of δ are obtained using informative and non-informative priors. A Monte Carlo simulation study is carried out for comparing the proposed methods of estimation. Finally, the methods developed are illustrated with a couple of real data examples.
MATHEMATICAL SUBJECT CLASSIFICATION 2010:
Acknowledgments
The authors express their sincere thanks to anonymous reviewer for his constructive comments and useful suggestions which led to improvement in the quality of this article.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
Hare Krishna http://orcid.org/0000-0002-2585-3232
Madhulika Dube http://orcid.org/0000-0003-0973-3043
Renu Garg http://orcid.org/0000-0002-5869-3386