Limit laws and mantissa distributions

• Autorzy: Sharpe M.
• Języki publikacji: EN

Abstrakty

EN

There are two main parts to the paper, both connected to Benford’s Law. In the first, we present a generalization of the averaging theorem of Flehinger. In the second, we study the connection between multiplicative infinite divisibility and Benford’s Law, ending with a variant of the Lindeberg-Feller theorem that describes a rather specific triangular array model leading to Benford behavior.

Słowa kluczowe

EN

Benford’s Law; mantissa; Flehinger’s theorem; log-normal; uniform; triangular array

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2006
• Tom: Vol. 26, Fasc. 1
• Strony: 175--185
• Opis fizyczny: Bibliogr. 6 poz., wykr.

Twórcy

autor

Sharpe M.

• UCSD, Mathematics Department, 9500 Gilman Dr La Jolla, CA 92093-0112, U.S.A.

Bibliografia

• [1] F. Benford, The law of anomalous numbers, Proc. Amer. Phil. Soc. 78 (1938), pp. 551-572.
• [2] B. J. Fiehinger, On the probability that a random integer has initial digit A, Amer. Math. Monthly 73 (10) (1966), pp. 1056-1061.
• [3] D. E. Knuth, The Art of Computer Programming, Vols. 2-3, Addison-Wesley, Reading, MA, 1997.
• [4] P. Lévy, Laddition des variables aléatoires définies sur une circonférence, Bull. Soc. Math. France 67 (1939), pp. 1-41.
• [5] H. Robbins, On the equidistribution of sums of independent random variables, Proc. Amer. Math. Soc. 4 (1953), pp. 786-799.
• [6] P. D. Scott and M. Fasli, Benford's law: An empirical investigation and a novel explanation, Technical report, Department of Computer Science, Univ. of Essex, 2001.