Newcomb–Benford law
E167726
The Newcomb–Benford law is a statistical principle stating that in many naturally occurring datasets, the leading digits are distributed logarithmically, with smaller digits (especially 1) appearing as the first digit more frequently than larger ones.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Benford | 1 |
| Benford's law | 1 |
| Newcomb–Benford law canonical | 1 |
| first-digit law | 1 |
Statements (52)
| Predicate | Object |
|---|---|
| instanceOf |
law of anomalous numbers
ⓘ
probability distribution law ⓘ statistical law ⓘ |
| alsoKnownAs |
Newcomb–Benford law
ⓘ
surface form:
Benford's law
Newcomb–Benford law ⓘ
surface form:
first-digit law
|
| appliesTo |
financial data
ⓘ
geographical data ⓘ many naturally occurring numerical datasets ⓘ physical constants ⓘ population numbers ⓘ scientific measurements ⓘ |
| BenfordContribution | collected large datasets to empirically confirm the law ⓘ |
| BenfordPublicationYear | 1938 ⓘ |
| category | empirical statistical regularity ⓘ |
| coreIdea | smaller leading digits occur more frequently than larger leading digits ⓘ |
| describes | distribution of leading digits in many real-world datasets ⓘ |
| doesNotTypicallyApplyTo |
assigned numbers such as telephone numbers
ⓘ
lottery numbers ⓘ numbers with fixed minimums and maximums ⓘ |
| field |
applied mathematics
ⓘ
probability theory ⓘ statistics ⓘ |
| historicalDeveloper | Frank Benford ⓘ |
| historicalPrecursor | Simon Newcomb ⓘ |
| leadingDigitDomain | d ∈ {1,2,3,4,5,6,7,8,9} ⓘ |
| leadingDigitProbabilityFormula | P(d) = log10(1 + 1/d) ⓘ |
| mathematicalBasis |
invariance under scale transformations
ⓘ
logarithmic distribution of leading digits ⓘ |
| NewcombObservation | logarithm tables were more worn at the beginning than at the end ⓘ |
| NewcombPublicationYear | 1881 ⓘ |
| predictsProbabilityOfLeadingDigit1 | approximately 0.301 ⓘ |
| predictsProbabilityOfLeadingDigit2 | approximately 0.176 ⓘ |
| predictsProbabilityOfLeadingDigit3 | approximately 0.125 ⓘ |
| predictsProbabilityOfLeadingDigit4 | approximately 0.097 ⓘ |
| predictsProbabilityOfLeadingDigit5 | approximately 0.079 ⓘ |
| predictsProbabilityOfLeadingDigit6 | approximately 0.067 ⓘ |
| predictsProbabilityOfLeadingDigit7 | approximately 0.058 ⓘ |
| predictsProbabilityOfLeadingDigit8 | approximately 0.051 ⓘ |
| predictsProbabilityOfLeadingDigit9 | approximately 0.046 ⓘ |
| property |
base invariance (approximately)
ⓘ
scale invariance ⓘ |
| relatedConcept |
Zipf's law
ⓘ
law of large numbers ⓘ mantissa distribution of logarithms ⓘ |
| typicalDatasetCondition |
data spanning several orders of magnitude
ⓘ
no artificial minimum or maximum constraints ⓘ |
| usedIn |
auditing
ⓘ
detection of data manipulation ⓘ election data analysis ⓘ forensic accounting ⓘ fraud detection ⓘ quality control of datasets ⓘ |
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Benford
this entity surface form:
Benford's law
this entity surface form:
first-digit law