Inferences on Weibull parameters with conventional type-I censoring

In this article we consider the statistical inferences of the unknown parameters of a Weibull distribution when the data are Type-I censored. It is well known that the maximum likelihood estimators do not always exist, and even when they exist, they do not have explicit expressions. We propose a simple fixed point type algorithm to compute the maximum likelihood estimators, when they exist. We also propose approximate maximum likelihood estimators of the unknown parameters, which have explicit forms. We construct the confidence intervals of the unknown parameters using asymptotic distribution and also by using the bootstrapping technique. Bayes estimates and the corresponding highest posterior density credible intervals of the unknown parameters are also obtained under fairly general priors on the unknown parameters. The Bayes estimates cannot be obtained explicitly. We propose to use the Gibbs sampling technique to compute the Bayes estimates and also to construct the highest posterior density credible intervals. Different methods have been compared by Monte Carlo simulations. One real data set has been analyzed for illustrative purposes.