Further revelations on L.S.D. (English) Zbl 0564.65028

Turner, Peter R.

IMA J. Numer. Anal. 4, 225-231 (1984).

This paper is concerned with the distribution of leading significant digits. In an earlier paper [IMA J. Numer. Anal. 2, 407-412 (1982; Zbl 0503.65029)] the author has already shown without any assumption of invariance to scaling that the results of successive multiplications give distributions which converge to the logarithmic distribution. Here, these results are extended to prove that the distribution remains invariant under further multiplicative or additive operations. This is a further step on the way to prove F. Benford’s conjecture [Proc. Am. Philos. Soc. 78, 551-572 (1938; Zbl 0018.26502)].

Reviewer: G.Schröder

MSC:

65G50	Roundoff error
62E20	Asymptotic distribution theory in statistics

Keywords:

distribution of leading significant digits; scaling

Citations:

Zbl 0503.65029; Zbl 0018.26502