Parameter and reliability estimation for an exponentiated half-logistic distribution under progressive type II censoring

Abstract

In this article, we deal with a two-parameter exponentiated half-logistic distribution. We consider the estimation of unknown parameters, the associated reliability function and the hazard rate function under progressive Type II censoring. Maximum likelihood estimates (M LEs) are proposed for unknown quantities. Bayes estimates are derived with respect to squared error, linex and entropy loss functions. Approximate explicit expressions for all Bayes estimates are obtained using the Lindley method. We also use importance sampling scheme to compute the Bayes estimates. Markov Chain Monte Carlo samples are further used to produce credible intervals for the unknown parameters. Asymptotic confidence intervals are constructed using the normality property of the MLEs. For comparison purposes, bootstrap-p and bootstrap-t confidence intervals are also constructed. A comprehensive numerical study is performed to compare the proposed estimates. Finally, a real-life data set is analysed to illustrate the proposed methods of estimation.

Keywords:

• Bayes estimates
• bootstrapping
• credible intervals
• importance sampling scheme
• Lindley approximation method
• maximum likelihood estimates
• progressive type II censoring

AMS Subject Classifications::

• 62F10
• 62F15
• 62F40
• 62N01

Acknowledgements

The authors are thankful to the referee for his valuable suggestions which have led to substantive improvements in the article.