Edgeworth series
E953116
The Edgeworth series is a statistical expansion used in probability theory to approximate probability distributions by correcting the normal distribution with higher-order cumulants.
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
asymptotic expansion
ⓘ
probability theory concept ⓘ statistical method ⓘ |
| appliesTo |
independent and identically distributed random variables
ⓘ
sums of random variables ⓘ |
| approximationOrder | can be extended to arbitrary finite order in 1/sqrt(n) ⓘ |
| assumes | existence of sufficiently high-order moments ⓘ |
| basedOn |
cumulants
ⓘ
moments of a distribution ⓘ |
| comparedWith | Gram–Charlier A series NERFINISHED ⓘ |
| domain |
continuous distributions
ⓘ
discrete distributions (via continuity corrections) ⓘ |
| expandsAround | normal distribution ⓘ |
| field |
mathematical statistics
ⓘ
probability theory ⓘ |
| generalizationOf | normal approximation ⓘ |
| goal | to approximate distribution functions more accurately than the normal distribution alone ⓘ |
| hasAdvantageOver | Gram–Charlier series in asymptotic justification ⓘ |
| hasProperty |
asymptotic in sample size
ⓘ
may not define a proper probability density for finite truncation ⓘ |
| historicalPublicationPeriod | late 19th century ⓘ |
| improves | rate of convergence of normal approximation ⓘ |
| namedAfter | Francis Ysidro Edgeworth NERFINISHED ⓘ |
| relatedTo |
Gram–Charlier series
NERFINISHED
ⓘ
central limit theorem NERFINISHED ⓘ saddlepoint approximation ⓘ |
| representation |
polynomial corrections to the normal density
ⓘ
series in powers of n^{-1/2} ⓘ |
| requires | standardization of the random variable ⓘ |
| usedBy |
applied probabilists
ⓘ
econometricians ⓘ statisticians ⓘ |
| usedFor |
approximating distribution of standardized sums
ⓘ
approximating probability distributions ⓘ approximating sampling distributions ⓘ refining normal approximation ⓘ |
| usedIn |
confidence interval approximation
ⓘ
econometrics ⓘ hypothesis testing ⓘ theoretical statistics ⓘ |
| usesConcept |
higher-order cumulants
ⓘ
kurtosis ⓘ skewness ⓘ standardized cumulants ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.