central limit theorem

E4991

probability theorem statistical theorem

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.

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All labels observed (8)

Label	Occurrences
central limit theorem canonical	19
Lyapunov central limit theorem	3
central limit theorem for martingales	2
Central Limit Theorem	1
Lindeberg central limit theorem	1
Lindeberg–Feller central limit theorem	1
classical central limit theorem	1
multivariate central limit theorem	1

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	Lindeberg central limit theorem ⓘ linked to: central limit theorem Lyapunov central limit theorem ⓘ linked to: central limit theorem central limit theorem for martingales ⓘ linked to: central limit theorem central limit theorem for triangular arrays ⓘ classical central limit theorem ⓘ functional central limit theorem ⓘ multivariate central limit theorem ⓘ linked to: 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

Referenced by (29)

Full triples — surface form annotated when it differs from this entity's canonical label.

Brownian motion → relatedConcept → central limit theorem ⓘ

central limit theorem → hasVariant → Lindeberg central limit theorem ⓘ

linked to: central limit theorem

central limit theorem → hasVariant → Lyapunov central limit theorem ⓘ

linked to: central limit theorem

central limit theorem → hasVariant → multivariate central limit theorem ⓘ

linked to: central limit theorem

central limit theorem → hasVariant → central limit theorem for martingales ⓘ

linked to: central limit theorem

Gaussian law of error → relatedTo → central limit theorem ⓘ

CLT → fullName → Central Limit Theorem ⓘ

linked to: central limit theorem

CLT → hasVariant → Lindeberg–Feller central limit theorem ⓘ

linked to: central limit theorem

CLT → hasVariant → Lyapunov central limit theorem ⓘ

linked to: central limit theorem

CLT → hasVariant → central limit theorem for martingales ⓘ

linked to: central limit theorem

Berry–Esseen theorem → refines → central limit theorem ⓘ

Berry–Esseen theorem → relatedTo → Lyapunov central limit theorem ⓘ

linked to: central limit theorem

law of large numbers → relatesTo → central limit theorem ⓘ

Probability theory → usesConcept → central limit theorem ⓘ

subject linked to: Probability Theory

Foundations of Probability → topic → central limit theorem ⓘ

Stirling's approximation → relatedTo → central limit theorem ⓘ

Andrew C. Berry → contributedTo → central limit theorem ⓘ

Khinchin's law of the iterated logarithm → refines → central limit theorem ⓘ

Limit Laws for Sums of Independent Random Variables → topic → central limit theorem ⓘ

Limit Laws for Sums of Independent Random Variables → relatedTo → classical central limit theorem ⓘ

linked to: central limit theorem

The Art of Probability for Scientists and Engineers → topic → central limit theorem ⓘ

LLN → contrastedWith → central limit theorem ⓘ

Lyapunov condition → usedIn → central limit theorem ⓘ

Probability via Expectation → topic → central limit theorem ⓘ

Calcul des probabilités → hasKeyConcept → central limit theorem ⓘ

Mathematical Methods of Statistics → topic → central limit theorem ⓘ

Cramér’s theorem in large deviations → relatedTo → central limit theorem ⓘ

Cramér–Wold theorem → relatedTo → central limit theorem ⓘ

Edgeworth series → relatedTo → central limit theorem ⓘ

All labels observed (8)

How this entity was disambiguated Show

Statements (50)

How these facts were elicited Show

Referenced by (29)

How this entity was disambiguated

How these facts were elicited