central limit theorem
E4991
The central limit theorem is a fundamental result in probability theory stating that the sum (or average) of many independent, identically distributed random variables tends to follow a normal distribution, regardless of the original variables’ distribution, under mild conditions.
All labels observed (8)
How this entity was disambiguated
This entity first appeared as the object of triple T79818 — 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: central limit theorem Context triple: [Brownian motion, relatedConcept, central limit theorem]
-
A.
Bose–Einstein statistics
Bose–Einstein statistics is a quantum statistical framework that describes the distribution and collective behavior of indistinguishable bosons, underpinning phenomena such as Bose–Einstein condensation.
-
B.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
-
C.
Stat.
Stat. is the standard legal citation abbreviation for the United States Statutes at Large, the official chronological compilation of all federal laws and resolutions enacted by the U.S. Congress.
-
D.
Shannon entropy
Shannon entropy is a fundamental measure in information theory that quantifies the average uncertainty or information content in a random variable or message source.
-
E.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
- 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: central limit theorem Target entity description: The central limit theorem is a fundamental result in probability theory stating that the sum (or average) of many independent, identically distributed random variables tends to follow a normal distribution, regardless of the original variables’ distribution, under mild conditions.
-
A.
Bose–Einstein statistics
Bose–Einstein statistics is a quantum statistical framework that describes the distribution and collective behavior of indistinguishable bosons, underpinning phenomena such as Bose–Einstein condensation.
-
B.
Feynman–Hellmann theorem
The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
-
C.
Stat.
Stat. is the standard legal citation abbreviation for the United States Statutes at Large, the official chronological compilation of all federal laws and resolutions enacted by the U.S. Congress.
-
D.
Shannon entropy
Shannon entropy is a fundamental measure in information theory that quantifies the average uncertainty or information content in a random variable or message source.
-
E.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
probability theorem
ⓘ
statistical theorem ⓘ |
| alsoKnownAs | CLT ⓘ |
| appliesTo |
identically distributed random variables
ⓘ
independent random variables ⓘ |
| approximationQuality | improves as sample size increases ⓘ |
| conclusionDistribution | normal distribution ⓘ |
| describes | convergence in distribution of normalized sums of random variables ⓘ |
| doesNotRequire | original distribution to be normal ⓘ |
| failsIf | variance is infinite ⓘ |
| field |
probability theory
ⓘ
statistics ⓘ |
| hasApplicationDomain |
econometrics
ⓘ
engineering ⓘ machine learning ⓘ physics ⓘ quantitative finance ⓘ |
| hasFormulation |
convergence of sample mean to normal distribution
ⓘ
convergence of standardized sum to standard normal distribution ⓘ |
| hasHistoricalContributor |
Abraham de Moivre
ⓘ
Aleksandr Lyapunov ⓘ Carl Friedrich Gauss ⓘ Jarl Waldemar Lindeberg ⓘ Pierre-Simon Laplace ⓘ |
| hasVariant |
central limit theorem
self-linksurface differs
ⓘ
surface form:
Lindeberg central limit theorem
central limit theorem self-linksurface differs ⓘ
surface form:
Lyapunov central limit theorem
central limit theorem self-linksurface differs ⓘ
surface form:
central limit theorem for martingales
central limit theorem for triangular arrays ⓘ classical central limit theorem ⓘ functional central limit theorem ⓘ central limit theorem self-linksurface differs ⓘ
surface form:
multivariate central limit theorem
|
| implies | approximate normality of sample mean for large samples ⓘ |
| isTypeOf |
convergence theorem
ⓘ
limit theorem ⓘ |
| relatedTo |
Berry–Esseen theorem
ⓘ
characteristic functions ⓘ law of large numbers ⓘ moment generating functions ⓘ stable distributions ⓘ |
| requiresCondition |
finite mean
ⓘ
finite variance ⓘ |
| statesThat | the standardized sum of many independent identically distributed random variables converges in distribution to a normal distribution ⓘ |
| underpins |
asymptotic normality of estimators
ⓘ
large-sample theory in statistics ⓘ |
| usedFor |
approximating sampling distributions
ⓘ
construction of confidence intervals ⓘ error analysis in Monte Carlo methods ⓘ hypothesis testing ⓘ normal approximation to Poisson distribution ⓘ normal approximation to binomial distribution ⓘ |
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: central limit theorem Description of subject: The central limit theorem is a fundamental result in probability theory stating that the sum (or average) of many independent, identically distributed random variables tends to follow a normal distribution, regardless of the original variables’ distribution, under mild conditions.
Referenced by (20)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Lindeberg central limit theorem
this entity surface form:
Lyapunov central limit theorem
this entity surface form:
multivariate central limit theorem
this entity surface form:
central limit theorem for martingales
this entity surface form:
Lindeberg–Feller central limit theorem
this entity surface form:
Lyapunov central limit theorem
this entity surface form:
central limit theorem for martingales
this entity surface form:
Lyapunov central limit theorem
subject surface form:
Probability theory
this entity surface form:
classical central limit theorem