Estimating reciprocals of scale parameters of two exponential populations with common location and ordered scales using censored samples

Abstract

The problem of estimating reciprocals of scale parameters (hazard rates) from two exponential populations with a common location and ordered scale parameters have been considered under the progressive type-II censoring scheme from a decision-theoretic viewpoint. The loss function is considered as quadratic. The maximum-likelihood estimators (MLEs) and the uniformly minimum variance unbiased estimators (UMVUEs) are derived. Sufficient conditions are derived for improving estimators in affine and scale equivariant classes. Consequently, improved estimators over the MLEs and the UMVUEs are derived. A numerical comparison among all the proposed estimators is made, and conclusions are drawn regarding their performances with respect to the quadratic loss function.

Keywords:

• Brewster–Zidek technique
• equivariant estimators
• progressive type-II censoring
• relative risk performance
• restricted MLE
• uniformly minimum variance unbiased estimator

Mathematics Subject Classifications 2010:

• 62F10
• 62C15
• 62F30
• 62N02

Acknowledgments

The authors would like to sincerely thank the two anonymous reviewers and an editor for their helpful comments and suggestions which have improved the presentation of the manuscript. The Second author (Manas Ranjan Tripathy) would like to thank Department of Science and Technology, SERB, [EMR/2017/003078], New Delhi, India, for providing some financial support.

Disclosure statement

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