Bayesian inference and prediction of the inverse Weibull distribution for type-II censored data.

*(English)*Zbl 1284.62604Summary: This paper describes the Bayesian inference and prediction of the inverse Weibull distribution for type-II censored data. First we consider the Bayesian inference of the unknown parameter under a squared error loss function. Although we have discussed mainly the squared error loss function, any other loss function can easily be considered. A Gibbs sampling procedure is used to draw Markov Chain Monte Carlo (MCMC) samples, and they have in turn, been used to compute the Bayes estimates and also to construct the corresponding credible intervals with the help of an importance sampling technique. We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. We further consider one-sample and two-sample Bayes prediction problems based on the observed sample and provide appropriate predictive intervals with a given coverage probability. A real life data set is used to illustrate the results derived. Some open problems are indicated for further research.

##### Keywords:

Bayes estimators; asymptotic distribution; type-I censoring; type-II censoring; Markov chain Monte Carlo; posterior predictive density
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\textit{D. Kundu} and \textit{H. Howlader}, Comput. Stat. Data Anal. 54, No. 6, 1547--1558 (2010; Zbl 1284.62604)

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