Approximate Bayes estimation of the parameters and reliability function of a mixture of two inverse Weibull distributions under Type-2 censoring

Abstract

The main goal of this paper is to develop the approximate Bayes estimation of the five-dimensional vector of the parameters and reliability function of a mixture of two inverse Weibull distributions (MTIWD) under Type-2 censoring. Usually, the posterior distribution is complicated under the scheme of Type-2 censoring and the integrals that are involved cannot be obtained in a simple explicit form. In this study, we use Lindley's [Approximate Bayesian method, Trabajos Estadist. 31 (1980), pp. 223–237] approximate form of Bayes estimation in the case of an MTIWD under Type-2 censoring. Later, we calculate the estimated risks (ERs) of the Bayes estimates and compare them with the corresponding ERs of the maximum-likelihood estimates through Monte Carlo simulation. Finally, we analyse a real data set using the findings.

Keywords:

• two-component mixture
• Lindley's procedure
• proper prior
• reliability functions
• maximum likelihood
• estimated risk
• Monte Carlo simulation

Acknowledgements

The authors thank the referees for their helpful comments, which improved the presentation of the paper. This project was supported by King Saud University, Deanship of Scientific Research, College of Science Research Center.