Article
Distribution of Leading Digits of Numbers
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Abstract
Applying the theory of distribution functions of sequences we find the relative densities of the first digits also for sequences xn not satisfy- ing Benford’s law. Especially for sequence xn = nr, n = 1, 2, . . . and xn = pr n, 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.
Keywords
Benford’s law, distribution function, prime number.
Citation
Ohkubo, Y. & Strauch, O. (2016). Distribution of leading digits of numbers. Uniform Distribution Theory, 11(1), 23–45. https://doi.org/10.1515/udt-2016-0003
Y. Ohkubo and O. Strauch, “Distribution of leading digits of numbers,” Uniform Distribution Theory, vol. 11, no. 1, pp. 23–45, 2016, doi: 10.1515/udt-2016-0003.
Ohkubo Y, Strauch O. Distribution of leading digits of numbers. Uniform Distribution Theory. 2016;11(1):23–45. doi:10.1515/udt-2016-0003.
Ohkubo, Y. and Strauch, O. (2016), ‘Distribution of leading digits of numbers’, Uniform Distribution Theory, 11(1), pp. 23–45. Available at: https://doi.org/10.1515/udt-2016-0003.
Ohkubo, Yukio, and Oto Strauch. “Distribution of Leading Digits of Numbers.” Uniform Distribution Theory, vol. 11, no. 1, 2016, pp. 23–45. https://doi.org/10.1515/udt-2016-0003.
Ohkubo, Yukio, and Oto Strauch. “Distribution of Leading Digits of Numbers.” Uniform Distribution Theory 11, no. 1 (2016): 23–45. https://doi.org/10.1515/udt-2016-0003.
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Published by: Engineering Journals
