On the study of negative cumulative copula extropy with applications

Multivariate datasets frequently arise in a wide range of real-world applications, where understanding and quantifying dependence structures among random variables is of fundamental importance. In recent years, copulas have attracted considerable attention as flexible tools for modelling such dependencies independently of marginal distributions. To effectively capture the uncertainty inherent in these dependence structures, a copula-based information measure is essential. In this paper, we introduce a multivariate extension of negative cumulative extropy (NCEx) based on copula and investigate its fundamental properties, including bounds, orthant ordering relationships, and convergence results. We also incorporate semi-parametric and nonparametric estimators for the proposed measure and evaluate their performance through Monte Carlo simulations. We further propose a novel dependence measure based on negative cumulative copula extropy (NCCEx), illustrating its behaviour through several simulated examples and real data applications. Additionally, a model selection criterion based on NCCEx is proposed, demonstrating its effectiveness in identifying an appropriate copula model for both simulated and real datasets. Finally, we illustrate the applicability of NCCEx through an application to financial risk analysis.