Preliminary Test and Shrinkage Estimations of Scale Parameters for Two Exponential Distributions based on Record Values

TL;DR

This paper investigates preliminary test and shrinkage estimators for the scale parameters of two exponential distributions using record values, optimizing significance levels and shrinkage coefficients for better estimation accuracy.

Contribution

It introduces optimal significance levels and shrinkage coefficients for estimators based on record values, enhancing estimation methods in reliability analysis.

Findings

Optimal significance level for preliminary test estimation identified.

Shrinkage coefficient values derived for improved estimation.

Method improves accuracy in estimating exponential distribution parameters.

Abstract

The exponential distribution is applied in a very wide variety of statistical procedures. Among the most prominent applications are those in the field of life testing and reliability theory. When there are two record samples available for estimating the scale parameter, a preliminary test is usually used to determine whether to pool the samples or use the individual sample. In this paper, the preliminary test estimator and shrinkage estimator are studied. The optimum level of significance for preliminary test estimation and the optimum values of shrinkage coefficient are obtained based on minimax regret criterion under the weighted square error loss function.