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

Articles in Press

Document Type : Original Article

Authors
Santosh Kumar Chaudhary 1
Nitin Gupta 2
1 Department of Statistics, Central University of Jharkhand, Ranchi, India.
2 Department of Mathematics, Indian Institute of Technology Kharagpur, India.
10.22034/jirss.2026.2082667.1175
Abstract
This paper proposes new nonparametric tests for symmetry based on cumulative past extropy and cumulative residual extropy of record values, motivated by a recent characterization of symmetric distributions by Gupta and Chaudhary (2024). The proposed estimators are inspired by the methodology introduced by Vasicek (1976). The proposed tests do not require estimation of the centre of symmetry, making them robust and easy to implement. Their asymptotic properties and consistency are established, and critical values are obtained via Monte Carlo simulations. Power is evaluated under various asymmetric alternatives. Results show that the proposed tests perform competitively and often outperform existing symmetry tests while maintaining the nominal significance level. Application of the test to six real-world datasets confirms its effectiveness in detecting symmetric and asymmetric behavior through significant p-values.
Keywords
Symmetry testing
Record values
Cumulative past extropy
Cumulative residual extropy
Nonparametric test
Subjects
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Journal of the Iranian Statistical Society

Articles in Press, Accepted Manuscript
Available Online from 29 June 2026

  • Receive Date 31 December 2025
  • Revise Date 15 June 2026
  • Accept Date 16 June 2026