Estimation of common location parameter of several heterogeneous exponential populations based on generalized order statistics

Abstract

In this article, several independent populations following exponential distribution with common location parameter and unknown and unequal scale parameters are considered. From these populations, several independent samples of generalized order statistics (gos) are drawn. Under the setup of gos, the problem of estimation of common location parameter is discussed and various estimators of common location parameter are derived. The authors obtained maximum likelihood estimator (MLE), modified MLE and uniformly minimum variance unbiased estimator of common location parameter. Furthermore, under scaled-squared error loss function, a general inadmissibility result of invariant estimator is proposed. The derived results are further reduced for upper record values which is a special case of gos. Finally, simulation study and real life example are reported to show the performances of various competing estimators in terms of percentage risk improvement.

Keywords:

• Upper record values
• modified maximum likelihood estimator
• uniformly minimum variance unbiased estimator
• Brewster–Zidek technique
• improved estimator

Acknowledgments

The authors are thankful to the anonymous referees and an associate editor for their constructive and helpful comments which led to a significantly improved presentation.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The second author would like to thank Science and Engineering Research Board, DST, Government of India [MATRICS Grant: MTR/2018/000084] for providing financial support.