Iranian Statistical Society Journal of the Iranian Statistical Society 1726-4057 24 2 2025 12 01 A Quantile Based Generalized Cross Entropy of Order Statistics 33 49 733689 10.22034/jirss.2025.2030759.1064 EN Rajesh Ganapathi Cochin University of Science and Technology Tincy Philip Cochin University of Science and Technology Journal Article 2024 05 31 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. https://jirss.irstat.ir/article_733689_a6fa0dc13c61dc928712789c96ee90a5.pdf