On Inadmissibility Results of Common Scale Parameters of $k(\ge2)$ Pareto Populations for Generalized Ordered Statistics

Accepted November 2025

Abstract

The paper addresses the estimation of a common scale parameter in $k(\geq 2)$ Pareto populations with unknown shape parameters, using generalized order statistics. Maximum likelihood, modified maximum likelihood, and uniformly minimum variance unbiased estimators are derived. A class of estimators, improving upon the maximum likelihood estimator, is introduced based on the minimum risk criterion with a scaled squared error loss function. The performance of the estimators is analyzed through simulations under progressive type II censoring, and two empirical datasets are used to demonstrate the practical application of the findings.