First-Digit Law in Nonextensive Statistics

Details First-Digit Law in Nonextensive Statistics First-Digit Law in Nonextensive Statistics

2010-10-13

arxiv.org/abs/1010.2699v1

Phys.Rev.E82:041110,2010

Physics

Data Analysis, Statistics and Probability

11 pages, 3 figures, published in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.82.041110

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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