Estimation of parameters of inverse Weibull distribution and application to multi-component stress-strength model

Abstract

The problem of estimation of the parameters of two-parameter inverse Weibull distributions has been considered. We establish existence and uniqueness of the maximum likelihood estimators of the scale and shape parameters. We derive Bayes estimators of the parameters under the entropy loss function. Hierarchical Bayes estimator, equivariant estimator and a class of minimax estimators are derived when shape parameter is known. Ordered Bayes estimators using information about second population are also derived. We investigate the reliability of multi-component stress-strength model using classical and Bayesian approaches. Risk comparison of the classical and Bayes estimators is done using Monte Carlo simulations. Applications of the proposed estimators are shown using real data sets.

Keywords:

• Maximum likelihood estimators
• equivariant estimator
• Bayes estimators
• ordered scale parameters
• UMVUE
• stress-strength reliability
• Monte Carlo simulations

2010 Mathematics Subject Classifications:

• 62F10
• 62F30
• 62N05

Acknowledgements

The authors express sincere gratitude to the reviewers, Associate Editor and Editor for their valuable comments which led to the substantial improvement of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Indian Institute of Technology (Indian School of Mines), Dhanbad [grant number FRS(125)/2018-19/AM]