Cumulative Residual Extropy of Minimum Ranked Set Sampling with Unequal Samples

TL;DR

This paper investigates the uncertainty measure called cumulative residual extropy (CREX) for minimum ranked set sampling with unequal samples, comparing it to simple random sampling and proposing new estimators and a disparity measure.

Contribution

It introduces CREX analysis for MinRSSU, develops new estimators, and proposes a novel measure to compare distributions of MinRSSU and SRS.

Findings

CREX provides insights into uncertainty in MinRSSU and SRS.

New estimators of CREX show improved bias and MSE.

Disparity measure effectively compares MinRSSU and SRS distributions.

Abstract

Recently, an alternative measure of uncertainty called cumulative residual extropy (CREX) was proposed by Jahanshahi et al. (2019). In this paper, we consider uncertainty measures of minimum ranked set sampling procedure with unequal samples (MinRSSU) in terms of CREX and its dynamic version and we compare the uncertainty and information content of CREX based on MinRSSU and simple random sampling (SRS) designs. Also, using simulation, we study on new estimators of CREX for MinRSSU and SRS designs in terms of bias and mean square error. Finally, we provide a new discrimination measure of disparity between the distribution of MinRSSU and parental data SRS.