Some properties on dynamic cumulative Tsallis residual entropy measures based on Sarmanov family with applications to motor data

This study presents Tsallis and Rényi entropies as continuous measures of information for continuous distributions based on concomitants of generalized order statistics from the Sarmanov (SAR) family. Additionally, the characteristics and their relationship to other information measures are presented. One of such measures is the cumulative Tsallis residual entropy (CTRE), which can be regarded as an alternative measure of dispersion, and we study its dynamic version. Moreover, applications of these results are given for order statistics, and the record values as special cases with uniform, Weibull, and exponential marginal distributions. Furthermore, the empirical alternative CTRE (denoted ACTRE) was proposed to estimate these information measures. Finally, a real-world dataset has been examined for illustrative purposes and demonstrates superior goodness-of-fit and interpretability compared with classical bivariate distributions.