Benfords Law

Author

Eric W. Weisstein
September 16, 2007

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Statistics/BenfordsLaw.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/BenfordsLaw.html.

©2007 Wolfram Research, Inc. except for portions noted otherwise

Distribution

d=Integrate[1/x,{x,D,D+1}]/Integrate[1/x,{x,1,10}]

FullSimplify[10^d]

Simplify[((-Log[D]+Log[1+D])/(Log[10]))-Log[10,1+(1/D)],D>0]

Normalization

P[d_]:=Log[10,1+1/d]

Simplify[Sum[P[d],{d,1,9}]]

Plot

<<BarCharts`

BarChart[Table[P[d],{d,1,9}],AxesLabel->{D,HoldForm[P[D]]}]