Dirichlet distribution
E466249
conjugate prior
continuous distribution
exponential family distribution
multivariate distribution
probability 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.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Dirichlet distribution canonical | 4 |
| Dirichlet distribution density | 1 |
| Dirichlet process | 1 |
| Dirichlet-multinomial distribution | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4746239 — 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: Dirichlet distribution Context triple: [Peter Gustav Lejeune Dirichlet, notableWork, Dirichlet distribution]
-
A.
Gaussian distribution
The Gaussian distribution, also known as the normal distribution, is a fundamental continuous probability distribution characterized by its symmetric bell-shaped curve and central role in statistics and the natural sciences.
-
B.
Pareto distribution
The Pareto distribution is a power-law probability distribution often used to model phenomena with heavy tails and strong inequality, such as wealth or city sizes.
-
C.
Tukey's lambda distribution
Tukey's lambda distribution is a flexible family of probability distributions used primarily for exploratory data analysis and modeling diverse shapes of data, including varying degrees of skewness and kurtosis.
-
D.
Cauchy distribution
The Cauchy distribution is a continuous probability distribution with heavy tails and undefined mean and variance, often used as a classic example of pathological behavior in probability theory and statistics.
-
E.
Gumbel
Gumbel is a surname most notably associated with American sportscaster Greg Gumbel.
- 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: Dirichlet distribution Target entity description: The Dirichlet distribution is a family of continuous multivariate probability distributions commonly used as a prior over categorical or multinomial parameters in Bayesian statistics.
-
A.
Gaussian distribution
The Gaussian distribution, also known as the normal distribution, is a fundamental continuous probability distribution characterized by its symmetric bell-shaped curve and central role in statistics and the natural sciences.
-
B.
Pareto distribution
The Pareto distribution is a power-law probability distribution often used to model phenomena with heavy tails and strong inequality, such as wealth or city sizes.
-
C.
Tukey's lambda distribution
Tukey's lambda distribution is a flexible family of probability distributions used primarily for exploratory data analysis and modeling diverse shapes of data, including varying degrees of skewness and kurtosis.
-
D.
Cauchy distribution
The Cauchy distribution is a continuous probability distribution with heavy tails and undefined mean and variance, often used as a classic example of pathological behavior in probability theory and statistics.
-
E.
Gumbel
Gumbel is a surname most notably associated with American sportscaster Greg Gumbel.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
conjugate prior
ⓘ
continuous distribution ⓘ exponential family distribution ⓘ multivariate distribution ⓘ probability distribution ⓘ |
| appearsIn |
Bayesian text modeling
ⓘ
document clustering ⓘ ecology ⓘ genetics ⓘ |
| belongsTo | multivariate continuous distributions ⓘ |
| belongsToFamily |
Dirichlet family
ⓘ
linked to:
Dirichlet
|
| conjugateTo |
categorical distribution
ⓘ
multinomial distribution ⓘ
linked to:
multinomial theorem
|
| definedOn | probability simplex ⓘ |
| field |
machine learning
ⓘ
probability theory ⓘ statistics ⓘ |
| generalizes | beta distribution ⓘ |
| hasDensityFunction | proportional to product of powers of components ⓘ |
| hasLimitingCase |
degenerate distribution on simplex as concentration goes to infinity
ⓘ
distribution concentrated on vertices of simplex as concentration goes to zero ⓘ |
| hasProperty |
components are nonnegative
ⓘ
components sum to 1 ⓘ exchangeable when parameters equal ⓘ mean equals normalized alpha parameters ⓘ variance decreases as concentration increases ⓘ |
| hasSpecialCase | beta distribution ⓘ |
| namedAfter | Peter Gustav Lejeune Dirichlet ⓘ |
| normalizingConstant | multivariate beta function ⓘ |
| parameterizedBy |
alpha vector
ⓘ
concentration parameters ⓘ |
| parameterSpace | positive real numbers ⓘ |
| relatedTo |
Dirichlet process
ⓘ
linked to:
Dirichlet process models
Dirichlet-multinomial distribution ⓘ
linked to:
Dirichlet distribution
|
| samplingMethod | normalized gamma variables ⓘ |
| support | k-dimensional probability simplex ⓘ |
| usedAs |
prior for categorical distribution
ⓘ
prior for multinomial distribution ⓘ |
| usedFor |
Bayesian inference for multinomial parameters
ⓘ
modeling uncertainty over discrete probability vectors ⓘ prior over mixture weights ⓘ prior over topic proportions ⓘ smoothing categorical frequency estimates ⓘ |
| usedIn |
Bayesian machine learning
ⓘ
linked to:
Bayesian inference
Bayesian mixture models ⓘ
linked to:
Bayesian nonparametrics
Bayesian nonparametrics ⓘ Bayesian statistics ⓘ
linked to:
Bayesian inference
Latent Dirichlet Allocation ⓘ topic modeling ⓘ |
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: Dirichlet distribution Description of subject: The Dirichlet distribution is a family of continuous multivariate probability distributions commonly used as a prior over categorical or multinomial parameters in Bayesian statistics.
Referenced by (7)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Dirichlet distribution
linked to: Dirichlet distribution
linked to: Dirichlet distribution