%I #45 Aug 06 2024 10:34:46

%S 3,4,4,0,2,3,6,9,6,7,1,2,3,2,0,6,2,4,8,8,2,5,2,3,8,7,6,0,0,3,9,9,4,4,

%T 4,0,9,1,0,6,7,7,2,8,5,8,1,4,0,5,9,9,8,8,6,3,1,4,3,3,7,7,1,8,2,9,8,1,

%U 8,0,8,1,3,3,1,6,7,2,9,2,8,4,8,4,0,4,5,1,5,3,6,8,5,2,9,2,9,1,8,8,3,7,2,6,1

%N Mean of leading digits in real-life sources of data, according to Benford's law (also called the first-digit law).

%D Scott, P., and Fasli, M. (2001). Benford's law: An empirical investigation and a novel explanation. Unpublished Manuscript.

%H Alois P. Heinz, <a href="/A213201/b213201.txt">Table of n, a(n) for n = 1..1000</a>

%H Steven Finch, <a href="/A213201/a213201.pdf">Newcomb-Benford Law</a>, August 17, 2011. [Cached copy, with permission of the author]

%H M. Grendar, G. Judge, L. Schechter, <a href="https://doi.org/10.1016/j.physa.2007.02.062">An empirical non-parametric likelihood family of data-based Benford-like distributions</a>, Physica A: Statistical Mechanics and its Applications, (2007) 380, 429-438.

%H G. Judge and L. Schechter, <a href="https://citeseerx.ist.psu.edu/pdf/a5f437f322d1ca9cd3551a601f80429c2d8583e0">Detecting problems in survey data using Benford's law</a>, Journal of Human Resources, Winter 2009, 44, 1-24.

%H Zhipeng Li, Lin Cong, and Huajia Wang, <a href="http://arxiv.org/abs/math/0408057">Discussion on Benford's Law and its Application</a>, arXiv:math/0408057 [math.ST], 2004.

%H I. Suh and T. C. Headrick, <a href="http://opensiuc.lib.siu.edu/epse_pubs/32/">A comparative analysis of the bootstrap versus traditional statistical procedures applied to digital analysis based on Benford's Law</a>, Journal of Forensic and Investigative Accounting, 2010, Vol. 2, No. 2, pp. 144-175.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Benford&#39;s_law">Benford's law</a>

%H <a href="/index/Be#Benford">Index entries for sequences related to Benford's law</a>

%F Equals Sum_{d=1..9} d*log(1+1/d)/log(10).

%e 3.44023696712320624882523876...

%t RealDigits[Log[10, 1562500/567], 10, 105][[1]] (* _Jean-François Alcover_, Nov 28 2018 *)

%o (MATLAB) digits(100);clear R;for i=1:9;R(i)=vpa([num2str(i) '*log10(1+1/' num2str(i) ')']);end;sum(R)

%o (MATLAB) vpa('2*log10(2)-4*log10(3)+8*log10(5)-log10(7)')

%o (PARI) sum(d=1, 9, d*log(1+1/d)/log(10)) \\ _Michel Marcus_, Nov 28 2018

%K nonn,cons

%O 1,1

%A _Joost de Winter_, Mar 01 2013