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24-04-2019 | Issue 3/2020

Annals of Data Science 3/2020

Statistical Inferences of \(R=P(X<Y)\) for Exponential Distribution Based on Generalized Order Statistics

Journal:
Annals of Data Science > Issue 3/2020
Authors:
M. J. S. Khan, Bushra Khatoon
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Abstract

In this paper, we have derived the classical and Bayesian inferences for stress–strength reliability \(R=P(X<Y)\), when the stress–strength data are available in the form of generalized order statistics (gos). It is supposed that the two random samples are mutually independent and obtained from the exponential population. Based on gos, maximum likelihood estimator (MLE) and uniformly minimum variance unbiased estimator (UMVUE) for R of the exponential distribution have been obtained. We have also constructed the exact confidence interval (CI) and asymptotic CI for R. In addition, we have derived the Bayes estimator for R by considering squared error loss function. Simulation study has been performed for comparing the performance of MLE and UMVUE. A Monte–Carlo simulation is also carried out for comparing the performance of Bayes estimator with different priors. For illustrative purposes, a real data analysis is also provided.

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