Estimating reciprocals of scale parameters of two exponential populations with common location and ordered scales using censored samples

Abstract

The problem of estimating reciprocals of scale parameters (hazard rates) from two exponential populations with a common location and ordered scale parameters have been considered under the progressive type-II censoring scheme from a decision-theoretic viewpoint. The loss function is considered as quadratic. The maximum-likelihood estimators (MLEs) and the uniformly minimum variance unbiased estimators (UMVUEs) are derived. Sufficient conditions are derived for improving estimators in affine and scale equivariant classes. Consequently, improved estimators over the MLEs and the UMVUEs are derived. A numerical comparison among all the proposed estimators is made, and conclusions are drawn regarding their performances with respect to the quadratic loss function.