Measures of statistical dispersion based on Shannon and Fisher information concepts

We propose and discuss two information-based measures of statistical dispersion of positive continuous random variables: the entropy-based dispersion and Fisher information-based dispersion. Although standard deviation is the most frequently employed dispersion measure, we show, that it is not well suited to quantify some aspects that are often expected intuitively, such as the degree of randomness. The proposed dispersion measures are not entirely independent, though each describes the quality of probability distribution from a different point of view. We discuss relationships between the measures, describe their extremal values and illustrate their properties on the Pareto, the lognormal and the lognormal mixture distributions. Application possibilities are also mentioned.