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Equations, Laws, and Functions of Applied Mathematics
Ist Teil von
The Princeton Companion to Applied Mathematics, 2015, p.135-172
Ort / Verlag
Princeton: Princeton University Press
Erscheinungsjahr
2015
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
Benford’s law, also known as thefirst-digit lawor thesignificant-digit law, is the empirical observation from statistical folklore that in many naturally occurring tables of numerical data the leading significant digits are not equally likely. In particular, more than 30% of the leading significant (nonzero) digits are 1 and less than 5% are 9.
Benford’s law asserts that, instead of being uniformly distributed, as might be expected, the first significant decimal digit often tends to follow the logarithmic distribution
\[\mathrm{Prob}(D_{1}=d)=\mathrm{log}_{10}\left ( \frac{d+1}{d} \right ),\; d=1,2,...,9\],
so
\[\mathrm{Prob}(D_{1}=1)=\mathrm{log}_{10}(2)=0.3010...,\]
\[\mathrm{Prob}(D_{1}=2)=\mathrm{log}_{10}(3/2)=0.1760...,\]
\[\vdots \]
\[\mathrm{Prob}(D_{1}=9)=\mathrm{log}_{10}(10/9)=0.04575...,\]
whereD
1represents the first significant decimal digit (e.g.,D
1(0.0203) =