First-digit law in nonextensive statistics

Lijing Shao and Bo-Qiang Ma
Phys. Rev. E 82, 041110 – Published 13 October 2010

Abstract

Nonextensive statistics, characterized by a nonextensive parameter q, is a promising and practically useful generalization of the Boltzmann statistics to describe power-law behaviors from physical and social observations. We here explore the unevenness of the first-digit distribution of nonextensive statistics analytically and numerically. We find that the first-digit distribution follows Benford’s law and fluctuates slightly in a periodical manner with respect to the logarithm of the temperature. The fluctuation decreases when q increases, and the result converges to Benford’s law exactly as q approaches 2. The relevant regularities between nonextensive statistics and Benford’s law are also presented and discussed.

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  • Received 25 June 2010

DOI:https://doi.org/10.1103/PhysRevE.82.041110

©2010 American Physical Society

Authors & Affiliations

Lijing Shao1 and Bo-Qiang Ma1,2,*

  • 1School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China
  • 2Center for High Energy Physics, Peking University, Beijing 100871, China

  • *Corresponding author. mabq@pku.edu.cn

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Vol. 82, Iss. 4 — October 2010

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