Dispersion indexes based on bivariate measures of uncertainty

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 bivariate 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 introduced in portfolio theory.