Noninformative priors for the ratio of the shape parameters of two Weibull distributions (original) (raw)

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.

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Authors and Affiliations

1. Department of Computer and Data Information, Sangji University, Wonju, 220-702, Korea
   Sang Gil Kang
2. Department of Asset Management, Daegu Haany University, Kyungsan, 712-715, Korea
   Woo Dong Lee
3. Department of Statistics, Kyungpook National University, Daegu, 702-701, Korea
   Yongku Kim

Authors

1. Sang Gil Kang
2. Woo Dong Lee
3. Yongku Kim

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Correspondence toYongku Kim.

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Kang, S.G., Lee, W.D. & Kim, Y. Noninformative priors for the ratio of the shape parameters of two Weibull distributions.Comput Stat 32, 35–50 (2017). https://doi.org/10.1007/s00180-015-0631-5

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• Received: 21 December 2014
• Accepted: 26 October 2015
• Published: 07 November 2015
• Issue date: March 2017
• DOI: https://doi.org/10.1007/s00180-015-0631-5

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