On Benford’s law. (English) Zbl 0555.62016

Nagasaka, Kenji

Ann. Inst. Stat. Math. 36, 337-352 (1984).

The author considers the set of all positive integers as a model population, which contains the set of significant figures of all possible physical constants, past, present and future. For polynomial sampling procedures, he proves that randomly sampled integers from the population do not necessarily obey F. Benford’s law [Proc. Am. Philos. Soc. 78, 551–572 (1938; Zbl 0018.26502)] but their Banach limit does. Benford’s law is also proved for geometrical sampling procedures and for linear recurrence sampling procedures.

Reviewer: J.Křivý

MSC:

62D05	Sampling theory, sample surveys
62E10	Characterization and structure theory of statistical distributions
11K16	Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.

Keywords:

first digits of random numbers; polynomial sampling procedures; randomly sampled integers; Banach limit; Benford’s law; geometrical sampling procedures; linear recurrence sampling procedures

Citations:

Zbl 0018.26502

References:

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