Negative cumulative residual extropy under concomitants of generalized order statistics based on Cambanis bivariate family with applications

Abstract Thermodynamics, statistical mechanics, and quantum mechanics are the branches of physics that use entropy and extropy measures. It also seems to quantify the degree of signal uncertainty in information theory. Recently, extropy has been widely used in the literature as a measure of dispersion or uncertainty. Within generalized Farlie-Gumbel-Morgenstern families, the Cambanis bivariate family holds a prominent position as an efficient and adaptable extended family. Motivated by this, our work gives numerous characterizations of Cambanis copula based on order statistics (OSs). Also, we study the negative cumulative residual extropy and various measures of information associated with it for concomitants generalized OSs.
Moreover, we study OSs and sequential OSs for each information measure in a computational study. This study offers a few beautiful symmetrical and asymmetric relationships that these information measures satisfy. Additionally, the empirical technique is applied to the Cambanis family to estimate every measure of negative extropy discussed in this work. As a final step, we have examined a bivariate real-world data set for illustrative purposes.