General weighted cumulative residual (past) extropy of minimum (maximum) ranked set sampling with unequal samples

TL;DR

This paper introduces new uncertainty measures called GWCRJ and GWCPJ for ranked set sampling methods with unequal samples, providing theoretical properties, stochastic comparisons, and empirical estimators.

Contribution

It develops the concepts of GWCRJ and GWCPJ for minRSSU and maxRSSU, including their properties and empirical estimators, advancing uncertainty quantification in ranked set sampling.

Findings

GWCRJ and GWCPJ are defined and their properties analyzed.

Stochastic comparison results for minRSSU and maxRSSU are established.

Empirical estimators for GWCRJ and GWCPJ are proposed.

Abstract

The general weighted cumulative residual extropy (GWCRJ) and general weighted cumulative past extropy (GWCPJ) are introduced in this paper. There are some results in relation to GWCPJ and GWCRJ. We take into account GWCRJ-based uncertainty measures for the minimal ranked set sampling technique with unequal samples (minRSSU). Additionally, we take into account GWCPJ-based uncertainty measures for the maximum ranked set sampling technique with unequal samples (maxRSSU). Stochastic comparison for Simple random sampling (SRS) is discussed. We looked at the monotone properties of minRSSU and maxRSSU as well as stochastic comparison. Finally, two empirical estimators of GWCPJ and GWCRJ are obtained.