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Randomness, evenness, and Rényi’s index

Author

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  • Eliazar, Iddo

Abstract

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.

Suggested Citation

  • Eliazar, Iddo, 2011. "Randomness, evenness, and Rényi’s index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 1982-1990.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:11:p:1982-1990
    DOI: 10.1016/j.physa.2010.11.008
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    Cited by:

    1. Chun-Xiao Nie, 2021. "Studying the correlation structure based on market geometry," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 16(2), pages 411-441, April.
    2. Nie, Chun-Xiao & Song, Fu-Tie & Li, Sai-Ping, 2016. "Rényi indices of financial minimum spanning trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 883-889.
    3. Nie, Chun-Xiao & Song, Fu-Tie, 2019. "Global Rényi index of the distance matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 902-915.
    4. Nie, Chun-Xiao, 2022. "Generalized correlation dimension and heterogeneity of network spaces," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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