Concomitant Extropy of Lai and Xie’s Extensions under Generalized Order Statistics: Properties, Estimation, and Application to Saudi Arabia Industrial Data

Abstract

In this work, we introduce and study the notion of concomitant extropy within the framework of generalized order statistics, extending the earlier contributions of Lai and Xie. The construction is supported with illustrative examples drawn from widely used probability distributions, highlighting the flexibility and applicability of the proposed measure. Several recurrence relations and important special cases are derived, providing further insights into the structure of the model. In addition, we explore the behavior of past and residual extropies associated with the model, and extend the analysis to include negative cumulative extropy as well as cumulative residual extropy. To complement the theoretical findings, a non-parametric estimation procedure is developed and applied to real-world Saudi Arabia Industrial data, demonstrating the practical utility and relevance of the proposed approach. The results indicate that concomitant extropy can serve as a valuable tool for modeling and analyzing uncertainty in diverse applied settings.