Classical and Bayesian Estimation of Stress-Strength Reliability from Generalized Inverted Exponential Distribution based on Upper Records

M.J.S. Khan, Bushra Khatoon

Abstract


This paper deals with the problem of classical and Bayesian estimation of stress-strength reliability (R=P(X<Y)) based on upper record values from generalized inverted exponential distribution (GIED). Hassan {et al.} (2018) discussed the maximum likelihood estimator (MLE) and Bayes estimator of $R$ by considering that the scale parameter to be known for defined distribution while we consider the case when all the parameters of GIED are unknown. In the classical approach, we have discussed MLE and uniformly minimum variance estimator (UMVUE). In Bayesian approach, we have considered the Bays estimator of R by considering the squared error loss function. Further, based on upper records, we have considered the Asymptotic confidence interval based on MLE, Bayesian credible interval and bootstrap confidence interval for $R$. Finally, Monte Carlo simulations and real data applications are being carried out for comparing the performances of the estimators of R.

Keywords


Generalized Inverted Exponential distribution, Stress-strength reliability, Maximum likelihood estimator, Bayes estimator, Confidence interval, Upper record values.

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DOI: http://dx.doi.org/10.18187/pjsor.v15i3.2716

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Title

Classical and Bayesian Estimation of Stress-Strength Reliability from Generalized Inverted Exponential Distribution based on Upper Records

Keywords

Generalized Inverted Exponential distribution, Stress-strength reliability, Maximum likelihood estimator, Bayes estimator, Confidence interval, Upper record values.

Description

This paper deals with the problem of classical and Bayesian estimation of stress-strength reliability (R=P(X<Y)) based on upper record values from generalized inverted exponential distribution (GIED). Hassan {et al.} (2018) discussed the maximum likelihood estimator (MLE) and Bayes estimator of $R$ by considering that the scale parameter to be known for defined distribution while we consider the case when all the parameters of GIED are unknown. In the classical approach, we have discussed MLE and uniformly minimum variance estimator (UMVUE). In Bayesian approach, we have considered the Bays estimator of R by considering the squared error loss function. Further, based on upper records, we have considered the Asymptotic confidence interval based on MLE, Bayesian credible interval and bootstrap confidence interval for $R$. Finally, Monte Carlo simulations and real data applications are being carried out for comparing the performances of the estimators of R.

Date

2019-09-07

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 15 No. 3, 2019



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810