✦ LIBER ✦

Randomness, evenness, and Rényi’s index

✍ Scribed by Iddo Eliazar

Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 235 KB
Volume: 390
Category: Article
ISSN: 0378-4371
DOI: 10.1016/j.physa.2010.11.008

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✦ Synopsis

This paper links together the notion of entropy and the notion of inequality indices-the former is applied in Statistical Physics to measure randomness, and the latter is applied in Economics to measure evenness. We explore the profound similarities between these diametric notions, construct a mathematical transformation between them, and show how randomness can be used to measure evenness -and vice versa. In particular, we devise and study Rényi's index-a randomness-based measure of evenness with special properties. Rényi's index is established as an effectual gauge of statistical heterogeneity in the context of general probability laws defined on the positive half-line.

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