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 |
How this entity was disambiguated
This entity first appeared as the object of triple T1465599 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Newcomb–Benford law Context triple: [Simon Newcomb, knownFor, Newcomb–Benford law]
-
A.
Statistical Independence in Probability, Analysis and Number Theory
"Statistical Independence in Probability, Analysis and Number Theory" is a mathematical monograph by Mark Kac that explores the concept of independence across probability theory, real analysis, and number theory.
-
B.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
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C.
Hardy–Ramanujan asymptotic formula
The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
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D.
Berry–Esseen theorem
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
-
E.
Bernoulli numbers
Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Newcomb–Benford law Target entity description: 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.
-
A.
Statistical Independence in Probability, Analysis and Number Theory
"Statistical Independence in Probability, Analysis and Number Theory" is a mathematical monograph by Mark Kac that explores the concept of independence across probability theory, real analysis, and number theory.
-
B.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
-
C.
Hardy–Ramanujan asymptotic formula
The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
-
D.
Berry–Esseen theorem
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
-
E.
Bernoulli numbers
Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
- F. None of above. chosen
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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Newcomb–Benford law Description of subject: 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.
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