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Objective Bayesian inference for the ratio of the scale parameters of two Weibull distributions

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  • Woo Dong Lee
  • Sang Gil Kang
  • Yongku Kim

Abstract

The Weibull distribution is widely used due to its versatility and relative simplicity. In our paper, the non informative priors for the ratio of the scale parameters of two Weibull models are provided. The asymptotic matching of coverage probabilities of Bayesian credible intervals is considered, with the corresponding frequentist coverage probabilities. We developed the various priors for the ratio of two scale parameters using the following matching criteria: quantile matching, matching of distribution function, highest posterior density matching, and inversion of test statistics. One particular prior, which meets all the matching criteria, is found. Next, we derive the reference priors for groups of ordering. We see that all the reference priors satisfy a first-order matching criterion and that the one-at-a-time reference prior is a second-order matching prior. A simulation study is performed and an example given.

Suggested Citation

  • Woo Dong Lee & Sang Gil Kang & Yongku Kim, 2017. "Objective Bayesian inference for the ratio of the scale parameters of two Weibull distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(10), pages 4943-4956, May.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:10:p:4943-4956
    DOI: 10.1080/03610926.2015.1091477
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    Cited by:

    1. Ramos, Eduardo & Ramos, Pedro L. & Louzada, Francisco, 2020. "Posterior properties of the Weibull distribution for censored data," Statistics & Probability Letters, Elsevier, vol. 166(C).

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