Measures of statistical dispersion based on Shannon and Fisher information concepts

KOŠŤÁL, Lubomír, Petr LÁNSKÝ and Ondřej POKORA. Measures of statistical dispersion based on Shannon and Fisher information concepts. INFORMATION SCIENCES. NEW YORK, NY 10010-1710 USA: ELSEVIER SCIENCE INC, 2013, vol. 235, JUN 20 2013, p. 214-223. ISSN 0020-0255. Available from: https://dx.doi.org/10.1016/j.ins.2013.02.023.

Basic information

• Original name: Measures of statistical dispersion based on Shannon and Fisher information concepts
• Authors: KOŠŤÁL, Lubomír, Petr LÁNSKÝ and Ondřej POKORA.
• Edition: INFORMATION SCIENCES, NEW YORK, NY 10010-1710 USA, ELSEVIER SCIENCE INC, 2013, 0020-0255.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10103 Statistics and probability
• Country of publisher: United States of America
• Confidentiality degree: is not subject to a state or trade secret
• Impact factor: Impact factor: 3.893
• Organization unit: Faculty of Science
• Doi: http://dx.doi.org/10.1016/j.ins.2013.02.023
• UT WoS: 000317887100015
• Keywords in English: Statistical dispersion; Entropy; Fisher information; Positive random variable
• Tags: International impact, Reviewed

Abstract

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.