New bounds on entropies based on order statistics and Gini’s mean difference

Abstract

Entropy measures are fundamental tool in information theory and various areas of sciences. We establish various lower bounds to the cumulative residual entropy and cumulative entropy based on Gini’s mean difference. Applying new results on upper bounds in Balakrishnan, Buono, and Longobardi (2022), we obtain sharper upper bounds for the cumulative residual entropy and cumulative entropy. New generalized cumulative residual entropy and cumulative entropy are also proposed.