Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. L. Adler and A.G. Konheim, Solution of Problem 4999, Amer. Math. Monthly 70 (1963), 218–219.
V. I. Arnol'd and A. Avez, Problèmes ergodiques de la mécanique classique, Gauthier-Villars, Paris 1967.
P. Billingsley, Ergodic theory and information, John Wiley and Sons, Inc., New York-London-Sydney 1965.
W. G. Brady, More on Benford's law, Fibonacci Quart. 16 (1978), 51–52.
J. L. Brown and R. L. Duncan, Modulo one uniform recurrence of the second order, Proc. Amer. Math. Soc. 50 (1975), 101–106.
J. G. van der Corput, Diophantische Ungleichungen, Acta Math. 56 (1931), 373–456.
P. Diaconis, The distribution of leading digits and uniform distribution mod 1, Ann. Prob. 5 (1977), 72–81.
R. L. Duncan, An application of uniform distributions to the Fibonacci numbers, Fibonacci Quart. 5 (1967), 137–140.
R. L. Duncan, Note on the initial digit problem, ibid. 7 (1969), 474–475.
B. J. Flehinger, On the probability that a random integer has initial digit A, Amer. Math. Monthly 73 (1966), 1056–1061.
K. Goto and T. Kano, Uniform distribution of some special sequences, Proc. Japan Acad. Ser. A Math. Sci. 61 (1985), 83–86.
G. H. Hardy, Divergent series, Oxford UP, London 1949.
A. Ja. Hincin, Continued fractions, The University of Chicago Press, Chicago, Ill.-London 1964.
P. Kiss and R. Tichy, Distribution of the ratios of the terms of a second order linear recurrence, to appear in Indag. Math.
L. Kuipers, Remark on a paper by R. L. Duncan concerning uniform distribution mod 1 of the sequence of logarithms of Fibonacci numbers, Fibonacci Quart. 7 (1969), 465–466, 473.
L. Kuipers and J.-S. Shiue, Remark on a paper by Duncan and Brown on the sequence of logarithms of certain recursive sequences, ibid. 11 (1973), 292–294.
L. Kuipers and H. Niederreiter, Uniform distribution of sequences, John Wiley and Sons, Inc., New York-London-Sydney-Toronto 1974.
L. Murata, On certain densities of sets of primes, Proc. Japan Acad. Ser. A Math. Sci. 56 (1980), 351–353; On some fundamental relatives among certain asymptotic densities, Math. Rep. Toyama Univ. 4 (1981), 47–61.
K. Nagasaka, On Benford's law, Ann. Inst. Stat. Math. 36 (1984), 337–352.
K. Nagasaka, Statistical properties of arithmetical sequences, Doctoral thesis, Tokyo Inst. Technology 1987.
K. Nagasaka and J.-S. Shiue, Benford's law for linear recurrence sequences, submitted to Tsukuba J. Math.
R. A. Raimi, The first digit problem, Amer. Math. Monthly 83 (1976), 521–538.
G. Rauzy, Propriétés statistiques de suites arithmétiques, Presses Univ. France, Paris 1976.
P. Schatte, Zur Verteilung der Mantissa der Gleichkommadarstellung einer Zerfallsgrösse, Z. Angew. Math. Mech. 53 (1973), 553–565.
P. Schatte, On H∞-summability and the uniform distribution of sequences, Math. Nachr. 113 (1983), 237–243.
P. Schatte, Estimates for the H∞-uniform distribution, preprint.
P. Schatte, On the uniform distribution of certain sequences and Benford's law, to appear in Math. Nachr.
L. C. Washington, Benford's law for Fibonacci and Lucas numbers, Fibonacci Quart. 19 (1981), 175–177.
R.E. Whitney, Initial digits for the sequence of primes, Amer. Math. Monthly 79 (1972), 150–152.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag
About this paper
Cite this paper
Kanemitsu, S., Nagasaka, K., Rauzy, G., Shiue, JS. (1988). On Benford's law: The first digit problem. In: Watanabe, S., Prokhorov, J.V. (eds) Probability Theory and Mathematical Statistics. Lecture Notes in Mathematics, vol 1299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078471
Download citation
DOI: https://doi.org/10.1007/BFb0078471
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18814-8
Online ISBN: 978-3-540-48187-4
eBook Packages: Springer Book Archive