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Limit laws and mantissa distributions. (English) Zbl 1108.60017

Summary: There are two main parts to the paper, both connected to F. Benford’s law [Proc. Am. Philos. Soc. 78, 551–572 (1938; Zbl 0018.26502)]. In the first we present a generalization of the averaging theorem of B. J. Flehinger [Am. Math. Mon. 73, 1056–1061 (1966; Zbl 0147.17502)]. 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 it rather specific triangular array model leading to Benford behavior.

MSC:

60F05 Central limit and other weak theorems
60E07 Infinitely divisible distributions; stable distributions
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