Bayesian inference for the Weibull distribution Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/td96k616g

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  • Bayesian inferential methods for the two parameter Weibull (and extreme-value distribution) are presented in a life-testing context. A practical method of calculating posterior distributions of the two parameters and a large class of functions of the parameters is presented. The emphasis is for the situation where the sample information is large relative to the prior information. The relationship between the fiducial method and the Bayesian method is examined and certain properties which are desirable from the frequentist point of view are shown for the Bayesian method. The frequency properties of the Bayesian method are examined under type I and type II progressive censoring by simulation and by exact methods. The probability of coverage of Bayesian confidence intervals, conditional on an ancillary event, is shown to be equal to the nominal probability of coverage, in the full sample case and under type II progressive censoring. Numerical examples of the Bayesian method were given, comparing the Bayesian results with results given by other methods.
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