Testing of symmetry based on cumulative past and residual extropy of record values

TL;DR

This paper introduces a new statistical test for symmetry in data distributions using cumulative past and residual extropy of record values, which is consistent and does not require estimating the center of symmetry.

Contribution

The paper develops a novel symmetry test based on extropy measures that simplifies the process by avoiding center estimation and demonstrates superior performance through simulations.

Findings

Test is consistent and reliable.

Performs better than existing symmetry tests.

Effective on real-life data sets.

Abstract

In this paper, we are testing the symmetry in the distribution of data observed on a random variable. We proposed test statistics using cumulative past and residual extropy of record values based on the characterization developed by Gupta and Chaudhary (2022) [5]. It is shown that the obtained estimator is consistent. Our proposed test has an advantage that we do not need to estimate the centre of symmetry. The empirical density, critical value and power of the proposed test statistics have been obtained. The test procedure has been implemented on six real-life data sets to verify its performance in identifying the symmetric nature. Simulations indicate our test performs better than the competitor tests.