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Erschienen in: Annals of Data Science 3/2020

24.04.2019

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

verfasst von: M. J. S. Khan, Bushra Khatoon

Erschienen in: Annals of Data Science | Ausgabe 3/2020

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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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Metadaten
Titel
Statistical Inferences of for Exponential Distribution Based on Generalized Order Statistics
verfasst von
M. J. S. Khan
Bushra Khatoon
Publikationsdatum
24.04.2019
Verlag
Springer Berlin Heidelberg
Erschienen in
Annals of Data Science / Ausgabe 3/2020
Print ISSN: 2198-5804
Elektronische ISSN: 2198-5812
DOI
https://doi.org/10.1007/s40745-019-00207-6

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