数字前导位数的分布

Uniform distribution theory Pub Date : 2016-06-01 DOI:10.1515/udt-2016-0003

Y. Ohkubo, O. Strauch

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引用次数: 5

摘要

摘要应用数列分布函数理论，得到了不满足本福德定律的数列xn的第一位数的相对密度。特别是对于序列xn = nr, n = 1,2，…xn=pnr $x_n = p_n^r $， n= 1,2，…，其中pn是所有素数的递增序列，r > 0是任意实数。我们还为这样的密度增加了收敛速率。

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Distribution of Leading Digits of Numbers

Abstract Applying the theory of distribution functions of sequences we find the relative densities of the first digits also for sequences xn not satisfying Benford’s law. Especially for sequence xn = nr, n = 1, 2, . . . and xn=pnr $x_n = p_n^r $ , n = 1, 2, . . ., where pn is the increasing sequence of all primes and r > 0 is an arbitrary real. We also add rate of convergence to such densities.

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Uniform distribution theory

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