A note on stochastic ordering of estimators of exponential reliability

TL;DR

This paper extends the understanding of stochastic ordering of maximum likelihood estimators in exponential reliability, demonstrating that MLEs under additional test plans are also stochastically ordered and exploring related applications.

Contribution

It broadens previous results by including new test plans and proves stochastic ordering of MLEs in these cases, with applications to reliability estimation.

Findings

MLEs are stochastically ordered under new test plans

Stochastic ordering holds beyond previously studied conditions

Applications demonstrate practical relevance in reliability estimation

Abstract

Recently Balakrishnan and Iliopoulos [Ann. Inst. Statist. Math. 61 (2009)] gave sufficient conditions under which maximum likelihood estimator (MLE) is stochastically increasing. In this paper we study test plans which are not considered there and we prove that MLEs for those plans are also stochastic ordered. We also give some applications to the estimation of reliability.