Wishart distribution
E728886
The Wishart distribution is a fundamental probability distribution over positive-definite matrices that generalizes the chi-squared distribution to multiple dimensions and underpins many multivariate statistical methods.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Wishart distribution canonical | 3 |
| Wishart matrices | 3 |
How this entity was disambiguated
This entity first appeared as the object of triple T8359640 — 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: Wishart distribution Context triple: [Hotelling’s T-squared distribution, relatedTo, Wishart distribution]
-
A.
Wishart
Wishart is a Scottish surname historically associated with notable figures in religion, politics, and academia.
-
B.
Hotelling’s T-squared distribution
Hotelling’s T-squared distribution is a multivariate generalization of Student’s t-distribution used primarily for hypothesis testing and constructing confidence regions for mean vectors in multivariate statistics.
-
C.
Pearson distribution
The Pearson distribution is a family of continuous probability distributions introduced by Karl Pearson to flexibly model data with varying skewness and kurtosis.
-
D.
Carsey-Werner Distribution
Carsey-Werner Distribution is a television distribution company best known for handling popular sitcoms produced by Carsey-Werner, including major hits from the late 1980s and 1990s.
-
E.
Dirichlet distribution
The Dirichlet distribution is a family of continuous multivariate probability distributions commonly used as a prior over categorical or multinomial parameters in Bayesian statistics.
- 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: Wishart distribution Target entity description: The Wishart distribution is a fundamental probability distribution over positive-definite matrices that generalizes the chi-squared distribution to multiple dimensions and underpins many multivariate statistical methods.
-
A.
Wishart
Wishart is a Scottish surname historically associated with notable figures in religion, politics, and academia.
-
B.
Hotelling’s T-squared distribution
Hotelling’s T-squared distribution is a multivariate generalization of Student’s t-distribution used primarily for hypothesis testing and constructing confidence regions for mean vectors in multivariate statistics.
-
C.
Pearson distribution
The Pearson distribution is a family of continuous probability distributions introduced by Karl Pearson to flexibly model data with varying skewness and kurtosis.
-
D.
Carsey-Werner Distribution
Carsey-Werner Distribution is a television distribution company best known for handling popular sitcoms produced by Carsey-Werner, including major hits from the late 1980s and 1990s.
-
E.
Dirichlet distribution
The Dirichlet distribution is a family of continuous multivariate probability distributions commonly used as a prior over categorical or multinomial parameters in Bayesian statistics.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
matrix-variate distribution
ⓘ
probability distribution ⓘ |
| appearsAs | likelihood of covariance matrix under multivariate normal sampling ⓘ |
| category | exponential family distribution ⓘ |
| conjugatePriorFor |
covariance matrix of multivariate normal distribution
ⓘ
precision matrix of multivariate normal distribution ⓘ |
| definedOn | space of symmetric positive-definite matrices ⓘ |
| degreesOfFreedomSymbol | n ⓘ |
| dimensionSymbol | p ⓘ |
| fullRankIf | n ≥ p ⓘ |
| generalizes | chi-squared distribution ⓘ |
| hasProperty |
degrees of freedom must exceed dimension minus one for finite mean
ⓘ
scale matrix must be positive-definite ⓘ support is convex cone ⓘ |
| hasRandomMatrixForm | X'X where X has independent multivariate normal rows ⓘ |
| introducedBy | John Wishart ⓘ |
| introducedInYear | 1928 ⓘ |
| isSpecialCaseOf | matrix gamma distribution ⓘ |
| logLikelihoodUsedIn | maximum likelihood estimation of covariance matrices ⓘ |
| mean | nS ⓘ |
| meanExistsIf | n > p - 1 ⓘ |
| namedAfter | John Wishart ⓘ |
| notation |
W_p(
u,
Sigma)
ⓘ
W_p(n, S) ⓘ |
| parameter |
degrees of freedom
ⓘ
dimension ⓘ scale matrix ⓘ |
| reductionToChiSquared | p = 1 ⓘ |
| relatedDistribution |
gamma distribution
ⓘ
inverse Wishart distribution ⓘ matrix normal distribution ⓘ multivariate normal distribution ⓘ |
| scaleMatrixSymbol | S ⓘ |
| support | symmetric positive-definite matrices ⓘ |
| usedAs | sampling distribution of sample covariance matrix ⓘ |
| usedIn |
Bayesian statistics
ⓘ
linked to:
Bayesian inference
Gaussian graphical models ⓘ
linked to:
probabilistic graphical models
covariance matrix estimation ⓘ econometrics ⓘ factor analysis ⓘ genetics ⓘ machine learning ⓘ multivariate analysis of variance ⓘ multivariate statistics ⓘ principal component analysis ⓘ random matrix theory ⓘ signal processing ⓘ |
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: Wishart distribution Description of subject: The Wishart distribution is a fundamental probability distribution over positive-definite matrices that generalizes the chi-squared distribution to multiple dimensions and underpins many multivariate statistical methods.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Wishart distribution
subject linked to:
Wishart
linked to: Wishart distribution
linked to: Wishart distribution