On the improved estimation of ordered parameters based on doubly type-II censored sample

TL;DR

This paper develops improved estimators for ordered parameters of two exponential distributions using doubly type-II censored samples, enhancing estimation accuracy under various loss functions through theoretical derivations and simulation validation.

Contribution

It introduces new estimators that outperform existing methods for ordered parameters in doubly censored exponential samples, including a generalized Bayes estimator and a class of improved estimators.

Findings

Improved estimators outperform BAEE in simulations.

The boundary estimator is a generalized Bayes estimator.

Application to real-life data demonstrates practical effectiveness.

Abstract

A doubly type-II censored scheme is an important sampling scheme in the life testing experiment and reliability engineering. In the present commutation, we have considered estimating ordered scale parameters of two exponential distributions based on doubly type-II censored samples with respect to a general scale invariant loss function. We have obtained several estimators that improve upon the BAEE. We also propose a class of improved estimators. It is shown that the boundary estimator of this class is generalized Bayes. As an application, we have derived improved estimators with respect to three special loss functions, namely quadratic loss, entropy loss, and symmetric loss function. We have applied these results to special life-testing sampling schemes. Finally, we conducted a simulation study to compare the performance of the improved estimators. A real-life data analysis has been considered for implementation purposes.