Symmetry being tested through simultaneous application of upper and lower k-records in extropy

Abstract

This study proposes a new test for testing the symmetry in the distribution of the data observed on a random variable. The test for symmetry has been constructed using a characterization result derived based on the extropy of k-records. The empirical density and critical values of the newly proposed test statistic have been obtained in this work. This study also analyses the performance of the test statistic based on the power values computed using Monte Carlo simulation methods and a comparison study with 10 competitor tests has been carried out. Moreover, the test procedure has been implemented on four real-life data sets to verify its performance in identifying the symmetric nature.

Keywords:

• Extropy
• k-records
• adjusted power
• symmetry
• testing of hypothesis

Mathematics Subject Classifications (2020):

• 62-08
• 62E10
• 62G10
• 94A17

Acknowledgments

We sincerely extend our thanks to the Editor, the Associate Editor and the Referee for the ample support and constructive comments that helped to improve the quality of the article to a great extent.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article or its supplementary materials.