Klimov Y. N.. On The Peculiarities Of The First Numbers (benford's Law)

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Submitted on: Aug 30, 2020, 07:32:41

Description: Abstracts: The contribution of V. I. Arnold to the statistics of the degree of two of the first digits is noted. The calculation of the powers of two for the first 100 digits is carried out to clarify the results of V. I. Arnold. The first 5 digits with the values o, 227 (table. 1) according to our calculations, they should have a value of 0.0791. In addition, the probability distribution of the first comer of degree two was modeled using simple algebraic equations of dynamics and cumulates, which were shown for dynamics F(n) to be from 0.2411 to 0.3498, and for cumulate KF(n) - 0.2697 to 0.3564. The study confirms the results of V. I. Arnold by the probability distribution of the first digits of powers of two, and the author - by the calculated probabilities of the first digit. Keywords: Benford's law, V. I. Arnold, statistics, power of two, first digit, refinement of probabilities of the first digit, mathematical modeling, simple algebraic equations

The Library of Congress (USA) reference page : http://lccn.loc.gov/cn2013300046.

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