Edgeworth expansion
E174595
Edgeworth expansion is an asymptotic series that refines the central limit theorem by providing higher-order approximations to the distribution of normalized sums of random variables.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Edgeworth expansion canonical | 1 |
| Gram–Charlier series | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1535800 — 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: Edgeworth expansion Context triple: [Berry–Esseen theorem, relatedTo, Edgeworth expansion]
-
A.
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.
-
B.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
-
C.
Frisch–Waugh–Lovell theorem
The Frisch–Waugh–Lovell theorem is a fundamental result in econometrics that shows how the coefficients of a multiple linear regression can be obtained by first partialling out (regressing out) other explanatory variables.
-
D.
Euler–Maclaurin summation formula
The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
-
E.
Laplace law of error
The Laplace law of error is a probability distribution characterized by a sharp peak at the mean and heavier tails than the normal distribution, historically used to model the magnitude of observational errors.
- 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: Edgeworth expansion Target entity description: Edgeworth expansion is an asymptotic series that refines the central limit theorem by providing higher-order approximations to the distribution of normalized sums of random variables.
-
A.
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.
-
B.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
-
C.
Frisch–Waugh–Lovell theorem
The Frisch–Waugh–Lovell theorem is a fundamental result in econometrics that shows how the coefficients of a multiple linear regression can be obtained by first partialling out (regressing out) other explanatory variables.
-
D.
Euler–Maclaurin summation formula
The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
-
E.
Laplace law of error
The Laplace law of error is a probability distribution characterized by a sharp peak at the mean and heavier tails than the normal distribution, historically used to model the magnitude of observational errors.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
asymptotic expansion
ⓘ
probability theory concept ⓘ statistical approximation method ⓘ |
| aimsTo | approximate tail probabilities more accurately than the normal approximation ⓘ |
| appliesTo | normalized sums of random variables ⓘ |
| approximates |
distribution function of standardized sums
ⓘ
probability density function of standardized sums ⓘ |
| assumes | independent and identically distributed summands in its classical form ⓘ |
| canBeExtendedTo | certain dependent data settings ⓘ |
| canBeWrittenAs | series involving standardized cumulants ⓘ |
| converges | asymptotically rather than absolutely in general ⓘ |
| field |
mathematical statistics
ⓘ
probability theory ⓘ |
| generalizes | normal approximation in the central limit theorem ⓘ |
| hasOrder |
first-order correction beyond the central limit theorem
ⓘ
second-order correction beyond the central limit theorem ⓘ |
| historicalDevelopment | originated in early 20th century work of Edgeworth and others ⓘ |
| improves | accuracy of normal approximation for finite samples ⓘ |
| includes |
kurtosis corrections
ⓘ
skewness corrections ⓘ |
| is |
an asymptotic series in powers of n^{-1/2}
ⓘ
typically truncated after a finite number of terms in applications ⓘ |
| isDiscussedIn | advanced textbooks on asymptotic statistics ⓘ |
| isOftenDerivedUsing |
characteristic functions
ⓘ
cumulant generating functions ⓘ |
| isRelatedTo |
Berry–Esseen theorem
ⓘ
Gram–Charlier series ⓘ
linked to:
Edgeworth expansion
saddlepoint approximation ⓘ |
| isUsedFor |
refined approximations to confidence interval coverage
ⓘ
refined approximations to distribution quantiles ⓘ refined approximations to p-values ⓘ |
| isUsedIn |
approximating sampling distributions
ⓘ
asymptotic statistics ⓘ higher-order asymptotics ⓘ statistical inference ⓘ |
| isValidAs | asymptotic approximation as sample size tends to infinity ⓘ |
| may | produce negative probabilities when truncated ⓘ |
| namedAfter | Francis Ysidro Edgeworth ⓘ |
| provides | higher-order approximations to probability distributions ⓘ |
| refines | central limit theorem ⓘ |
| requires |
existence of sufficiently high-order moments
ⓘ
regularity conditions on the underlying distribution ⓘ |
| uses |
Hermite polynomials
ⓘ
linked to:
Hermite functions
cumulants of random variables ⓘ moments of random variables ⓘ |
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: Edgeworth expansion Description of subject: Edgeworth expansion is an asymptotic series that refines the central limit theorem by providing higher-order approximations to the distribution of normalized sums of random variables.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Edgeworth expansion