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

Shuvashree Mondal and Debasis Kundu ()
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Shuvashree Mondal: Indian Institute of Technology Kanpur
Debasis Kundu: Indian Institute of Technology Kanpur

Sankhya B: The Indian Journal of Statistics, 2019, vol. 81, issue 1, No 1, 25 pages

Abstract: 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: Joint progressive censoring scheme; Weibull distribution; Beta-gamma distribution; Log-concave density function; Posterior analysis; Primary 62N01; 62N02; Secondary 62F10. (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s13571-017-0134-1

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