Sankhya B

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Point and Interval Estimation of Weibull Parameters Based on Joint Progressively Censored Data

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Abstract

The analysis of progressively censored data has received considerable attention in the last few years. In this paper, we consider the joint progressive censoring scheme for two populations. It is assumed that the lifetime distribution of the items from the two populations follows Weibull distribution with the same shape but different scale parameters. Based on the joint progressive censoring scheme, first, we consider the maximum likelihood estimators of the unknown parameters whenever they exist. We provide the Bayesian inferences of the unknown parameters under a fairly general priors on the shape and scale parameters. The Bayes estimators and the associated credible intervals cannot be obtained in closed form, and we propose to use the importance sampling technique to compute the same. Further, we consider the problem when it is known a priori that the expected lifetime of one population is smaller than the other. We provide the order-restricted classical and Bayesian inferences of the unknown parameters. Monte Carlo simulations are performed to observe the performances of the different estimators and the associated confidence and credible intervals. One real data set has been analyzed for illustrative purpose.

Keywords and phrases

Joint progressive censoring scheme Weibull distribution Beta-gamma distribution Log-concave density function Posterior analysis 

AMS (2000) subject classification

Primary 62N01, 62N02 Secondary 62F10. 

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Notes

Acknowledgements

The authors would like to thank the Editor-in-Chief Prof. D. Dey for providing several important suggestions which have helped to improve the manuscript significantly.

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Copyright information

© Indian Statistical Institute 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsIndian Institute of Technology KanpurPinIndia

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