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Study Of A Measure Of Efficiency As A Tool For Applying The Principle Of Least Effort To The Derivation Of The Zipf And The Pareto Laws

Author

Listed:
  • A. EL KAABOUCHI

    (ESTACA, Parc Universitaire Laval-Changé, Rue Georges Charpak, 53000 Laval, France)

  • F. X. MACHU

    (��Laboratoire SCIQ, ESIEA, 9 Rue Vésale, 75005 Paris, France)

  • J. COCKS

    (��Laboratoire SCIQ, ESIEA, 9 Rue Vésale, 75005 Paris, France)

  • R. WANG

    (��Laboratoire SCIQ, ESIEA, 9 Rue Vésale, 75005 Paris, France)

  • Y. Y. ZHU

    (�College of Mathematics and Computer Science, Wuhan Textile University, Wuhan, P. R. China)

  • Q. A. WANG

    (��Laboratoire SCIQ, ESIEA, 9 Rue Vésale, 75005 Paris, France‡IMMM, CNRS UMR 6283, Le Mans Université, Ave. O. Messiaen, 72085 Le Mans, France)

Abstract

The principle of least effort (PLE) is believed to be a universal rule for living systems. Its application to the derivation of the power law probability distributions of living systems has long been challenging. Recently, a measure of efficiency was proposed as a tool of deriving Zipf’s and Pareto’s laws directly from the PLE. This work is a further investigation of this efficiency measure from a mathematical point of view. The aim is to get further insight into its properties and usefulness as a metric of performance. We address some key mathematical properties of this efficiency such as its sign, uniqueness and robustness. We also look at the relationship between this measure and other properties of the system of interest such as inequality and uncertainty, by introducing a new method for calculating nonnegative continuous entropy.

Suggested Citation

  • A. El Kaabouchi & F. X. Machu & J. Cocks & R. Wang & Y. Y. Zhu & Q. A. Wang, 2021. "Study Of A Measure Of Efficiency As A Tool For Applying The Principle Of Least Effort To The Derivation Of The Zipf And The Pareto Laws," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 24(07n08), pages 1-20, December.
    • Handle: RePEc:wsi:acsxxx:v:24:y:2021:i:07n08:n:s0219525921500132
    DOI: 10.1142/S0219525921500132
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