Estimating order scale parameters of two scale mixture of exponential distributions

TL;DR

This paper develops improved estimators for the ordered scale parameters of two scale mixture exponential distributions under Stein and symmetric loss, demonstrating their superiority through theoretical proofs and simulation studies.

Contribution

It introduces new estimators that dominate existing affine equivariant estimators for two scale mixture exponential distributions, including boundary and generalized Bayes estimators.

Findings

Proved inadmissibility of certain estimators under Stein loss.

Constructed estimators that outperform the best affine equivariant estimators.

Validated improved estimators through simulation studies.

Abstract

Estimation of the ordered scale parameter of a two scale mixture of the exponential distribution is considered under Stein loss and symmetric loss. Under certain conditions, we prove that the inadmissibility equivariant estimator exhibits several improved estimators. Consequently, we propose various estimators that dominate the best affine equivariant estimators (BAEE). Also, we propose a class of estimators that dominates BAEE. We have proved that the boundary estimator of this class is a generalized Bayes estimator. The results are applied to the multivariate Lomax distribution and the Exponential Inverse Gaussian (E-IG) distribution. Consequently, we have obtained improved estimators for the ordered scale parameters of two multivariate Lomax distributions and the exponential inverse Gaussian distribution. For each case, we have conducted a simulation study to compare the risk performance of the improved estimators.