Measures of cumulative residual Tsallis entropy for concomitants of generalized order statistics based on the Morgenstern family with application to medical data

Ever since Tsallis introduced Tsallis entropy theory, it has been applied to a wide variety of topics in physics and chemistry, with new applications being discovered annually. The amount of research suggests that the Tsallis entropy concept holds significant potential. This paper introduces weighted cumulative residual Tsallis entropy (WCRTE) and weighted cumulative past Tsallis entropy (WCPTE), as well as their dynamic counterparts for the concomitants of $ m $-generalized order statistics ($ m $-GOSs) derived from the Farlie-Gumbel-Morgenstern bivariate family. The characteristics of the proposed entropy measures were analyzed, demonstrating their ability to characterize the Pareto and exponential distributions. Applications of these findings were presented for order statistics (OSs) systems and record values with uniform, Weibull, and power marginal distributions. Furthermore, the empirical alternatives WCRTE and WCPTE were proposed for calculating new information measures. Two real-world data sets have been evaluated for illustrative purposes, demonstrating satisfactory performance.