Abstract

We consider statistical inference of the unknown parameters of a two-parameter bathtub-shaped distribution (Chen, 2000) [Stat. & Prob. Letters 49 (2000) 155-161]. The inference will be conducted for Type-II censored and progressively Type-II censored data using the maximum likelihood and Bayes techniques. There are no explicit expressions for the estimators of the parameters. In the case of the maximum likelihood estimator (MLE), we propose a simple fixed point algorithmto compute the MLE and construct different confidence intervals and confidence regions of the unknown parameters. Bayes analyses of the unknown parameters are also discussed under fairly general priors for the unknown parameters.We propose to use the Markov Chain Monte Carlo (MCMC) and simulation-based technique to compute the Bayes estimates and the two-sided Bayesian probability intervals of the parameters. Also, we use the rejection sampling algorithm to produce the exact Bayes estimates. The methods developed will be applied in the analyses of two real data sets and a simulated data set. A Monte Carlo simulation is used to compare the results from the MLE and Bayes techniques.

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