×

zbMATH — the first resource for mathematics

Benford’s law for exponential random variables. (English) Zbl 1116.60315
Summary: Benford’s law assigns the probability \(\log_{10}(1+1/d)\) for finding a number starting with specific significant digit \(d\). We show that exponentially distributed numbers obey this law approximatively, i.e., within bounds of 0.03.

MSC:
60E99 Distribution theory
60C05 Combinatorial probability
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abramowitz, M.; Stegun, I., Handbook of mathematical functions, vol. 55, applied mathematics series, (1964), National Bureau of Standards Washington, DC · Zbl 0171.38503
[2] Benford, F., The law of anomalous numbers, Proc. amer. philos. soc., 78, 551-572, (1938)
[3] Diaconis, P., The distribution of leading digits and uniform distribution mod 1, Ann. probab., 5, 1, 72-81, (1977) · Zbl 0364.10025
[4] Duncan, R.L., A note on the initial digit problem, Fibonacci quart., 7, 5, 474-475, (1969) · Zbl 0215.06706
[5] Hill, T.P., A statistical derivation of the significant-digit law, Statist. sci., 10, 4, 354-363, (1995) · Zbl 0955.60509
[6] Hill, T.P., The first digit phenomenon, Amer. sci., 86, 358-363, (1998)
[7] Knuth, D., 1969. The Art of Computer Programming, Vol. 2. Addison-Wesley, Reading, MA, pp. 219-229.
[8] Leemis, L.M.; Schmeiser, B.W.; Evans, D.L., Survival distributions satisfying Benford’s law, Amer. statist., 54, 3, 1-6, (2000)
[9] Newcomb, S., Note on the frequency of use of the different digits in natural numbers, Amer. J. math., 4, 39-40, (1881) · JFM 13.0161.01
[10] Raimi, R., The first digit problem, Amer. math. monthly, 102, 322-327, (1976)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.