On weighted cumulative residual extropy and weighted negative cumulative extropy

TL;DR

This paper introduces new weighted measures of residual and negative extropy, provides estimators for complete and censored data, and explores their connections to reliability theory and systems.

Contribution

It defines general weighted cumulative residual and negative extropy, develops estimators for various data types, and links these measures to reliability and system coherence.

Findings

Derived simple estimators for complete and censored data

Established connections to reliability theory

Proposed empirical estimators for weighted negative cumulative extropy

Abstract

In this paper, we define general weighted cumulative residual extropy (GWCRJ) and general weighted negative cumulative extropy (GWNCJ). We obtain its simple estimators for complete and right censored data. We obtain some results on GWCREJ and GWNCJ. We establish its connection to reliability theory and coherent systems. We also propose empirical estimators of weighted negative cumulative extropy (WNCJ).