A Quantile Based Generalized Cross Entropy of Order Statistics

Document Type : Original Article

Authors
Rajesh Ganapathi
Tincy Philip
Cochin University of Science and Technology
10.22034/jirss.2025.2030759.1064
Abstract
In this paper, we propose a generalized cross entropy between the distributions of the ith order statistic and the parent random variable X, defined using the quantile function. This method is more flexible than traditional PDF-based measures, particularly in situations where estimating the underlying density is difficult or unreliable. We investigate the properties of this measure and present examples to illustrate these concepts. Furthermore, we introduce a residual version of the quantile based generalized cross entropy between the distributions of the ith order statistic and the parent random variable X, along with some characterization results. Comparative analyses using simulation and real data indicate that the proposed measure provides improved interpretability and robustness relative to the quantile based Kerridge inaccuracy measure. This study effectively connects theoretical development with practical application, contributing to the field of statistical analysis.
Keywords
Entropy
Cross Entropy
Order Statistics
Quantile Function
Hazard Function
Subjects
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Journal of the Iranian Statistical Society
Volume 24, Issue 2
December 2025
Pages 33-49

  • Receive Date 31 May 2024
  • Revise Date 04 November 2025
  • Accept Date 15 December 2025