Residual Tsallis Entropy and Record Values: Some New Insights

Recently, the uncertainty aspects of record values have been increasingly studied in the literature. In this paper, we study the residual Tsallis entropy of upper record values coming from random samples. In the continuous case, we define the Tsallis entropy quantity for the residual lifetime of upper record values in general distributions as the residual Tsallis entropy of upper record values coming from a uniform distribution. We also obtain a lower bound on the residual Tsallis entropy of upper data set values originating from an arbitrary continuous probability distribution. We also discuss the monotonic property of the residual Tsallis entropy of upper data sets.