Dispersion indices based on Kerridge inaccuracy and Kullback-Leibler divergence

The concept of varentropy has been recently introduced as a dispersion index of the reliability of measure of information. In this paper, we introduce new measures of variability for two measures of uncertainty, the Kerridge inaccuracy measure and the Kullback-Leibler divergence. These new definitions and related properties, bounds and examples are presented. Finally we show an application of Kullback-Leibler divergence and its dispersion index using the mean-variance rule.