Some characterizations of continuous symmetric distributions based on extropy of record values

TL;DR

This paper characterizes continuous symmetric distributions using various extropy measures of record values, extending previous results and demonstrating that symmetry can be identified through equal information in upper and lower record extropies.

Contribution

It introduces new characterizations of symmetric distributions based on different extropy measures of record values, expanding on prior work by Ahmadi (2021).

Findings

Symmetric distributions are characterized by equal extropy in upper and lower record values.

Different types of extropies, including residual and generalized residual extropy, are used for characterization.

The results extend existing characterizations and include measures like Kerridge inaccuracy.

Abstract

Using different extropies of k record values various characterizations are provided for continuous symmetric distributions. The results are in addition to the results of Ahmadi, J. (Statistical Papers, 2021, 62:2603-2626). These include cumulative residual (past) extropy, generalised cumulative residual (past) extropy, also some common Kerridge inaccuracy measures. Using inaccuracy extropy measures, it is demonstrated that continuous symmetric distributions are characterised by an equality of information in upper and lower k-records.