Noninformative priors for the ratio of the shape parameters of two Weibull distributions

Sang Gil Kang, Woo Dong Lee and Yongku Kim ()
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Sang Gil Kang: Sangji University
Woo Dong Lee: Daegu Haany University
Yongku Kim: Kyungpook National University

Computational Statistics, 2017, vol. 32, issue 1, No 2, 35-50

Abstract: Abstract The Weibull distribution is one of the most widely used lifetime distributions in reliability engineering. Here, the noninformative priors for the ratio of the shape parameters of two Weibull models are introduced. The first criterion used is the asymptotic matching of the coverage probabilities of Bayesian credible intervals with the corresponding frequentist coverage probabilities. We develop the probability matching priors for the ratio of the shape parameters using the following matching criteria: quantile matching, matching of the distribution function, highest posterior density matching, and matching via inversion of the test statistics. We obtain one particular prior that meets all the matching criteria. Next, we derive the reference priors for different groups of ordering. Our findings show that some of the reference priors satisfy a first-order matching criterion and the one-at-a-time reference prior is a second-order matching prior. Lastly, we perform a simulation study and provide a real-world example.

Keywords: Matching prior; Reference prior; Ratio of shape parameters; Weibull distribution (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00180-015-0631-5

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