Bayesian and maximum likelihood estimations of the inverse Weibull parameters under progressive type-II censoring

Abstract

In this paper, the statistical inference of the unknown parameters of a two-parameter inverse Weibull (IW) distribution based on the progressive type-II censored sample has been considered. The maximum likelihood estimators (MLEs) cannot be obtained in explicit forms, hence the approximate MLEs are proposed, which are in explicit forms. The Bayes and generalized Bayes estimators for the IW parameters and the reliability function based on the squared error and Linex loss functions are provided. The Bayes and generalized Bayes estimators cannot be obtained explicitly, hence Lindley's approximation is used to obtain the Bayes and generalized Bayes estimators. Furthermore, the highest posterior density credible intervals of the unknown parameters based on Gibbs sampling technique are computed, and using an optimality criterion the optimal censoring scheme has been suggested. Simulation experiments are performed to see the effectiveness of the different estimators. Finally, two data sets have been analysed for illustrative purposes.

Keywords:

• Bayes estimation
• Lindley approximation
• maximum likelihood estimation
• reliability function
• squared error and Linex loss function
• estimated risk and Monte Carlo simulation
• Gibbs samples

Acknowledgements

The authors would like to thank the referees for their valuable suggestion, and the editor-in-chief Prof. R.G. Krutchkoff for his encouragement. This project was supported by King Saud University, Deanship of Scientific Research, College of Science Research Center.