Abstract
Several generalizations of Shannon entropy have been introduced in the literature. One of such a measure is the cumulative residual Tsallis entropy (CRTE) which can be viewed as an alternative dispersion measure. In this paper, we obtain some further results for such a measure, in relation with the cumulative residual Tsallis entropy and with the variance of random variables. Specifically, we present new equivalent expressions, bounds, normalized CRTE, connection to the differential entropy and excess wealth transform and stochastic comparisons involving such measures. Besides, the dynamic version of such under consideration measure is elaborated and some monotonicity results are also given. Finally, we consider the problem of estimating the CRTE by means of the empirical CRTE. In this regard, we use two different empirical estimators of cumulative distribution function to estimate CRTE. Then, we study practical results of the second estimator in blind image quality assessment. (C) 2021 Published by Elsevier B.V.
NSTL
Elsevier