chi-square distribution
E596523
The chi-square distribution is a continuous probability distribution commonly used in statistics to model the sum of squared standard normal variables and to conduct hypothesis tests such as goodness-of-fit and tests of independence.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Pearson's chi-squared test | 1 |
| chi-square distribution canonical | 1 |
| chi-squared distribution | 1 |
| chi-squared test | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6482582 — 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: chi-square distribution Context triple: [Gamma function, appearsIn, chi-square distribution]
-
A.
F-distribution
The F-distribution is a continuous probability distribution widely used in statistics, especially for comparing variances and conducting analysis of variance (ANOVA) tests.
-
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.
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.
-
D.
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.
-
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: chi-square distribution Target entity description: The chi-square distribution is a continuous probability distribution commonly used in statistics to model the sum of squared standard normal variables and to conduct hypothesis tests such as goodness-of-fit and tests of independence.
-
A.
F-distribution
The F-distribution is a continuous probability distribution widely used in statistics, especially for comparing variances and conducting analysis of variance (ANOVA) tests.
-
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.
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.
-
D.
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.
-
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 |
probability distribution
ⓘ
right-skewed distribution ⓘ |
| assumes |
independent observations in contingency tables
ⓘ
sufficiently large expected cell counts for chi-square approximation ⓘ |
| belongsTo | family of Pearson distributions ⓘ |
| cdf | regularized gamma function of x/2 and k/2 ⓘ |
| characteristicFunction | φ(t) = (1 - 2it)^{-k/2} ⓘ |
| cumulativeShape | increasing and concave for small x ⓘ |
| definedOn | nonnegative real numbers ⓘ |
| hasProperty |
approaches normal distribution as degrees of freedom increase
ⓘ
nonnegative random variable ⓘ right-skewness decreases as degrees of freedom increase ⓘ |
| hasScaleParameter | 2 in gamma representation ⓘ |
| hasShapeParameter | k/2 in gamma representation ⓘ |
| introducedBy | Karl Pearson ⓘ |
| isSpecialCaseOf | gamma distribution ⓘ |
| kurtosisExcess | 12/k ⓘ |
| mean | k (degrees of freedom) ⓘ |
| mode | k - 2 for k ≥ 2 ⓘ |
| momentGeneratingFunction | M(t) = (1 - 2t)^{-k/2} for t < 1/2 ⓘ |
| origin |
distribution of quadratic forms in normal variables
ⓘ
sum of squares of independent standard normal variables ⓘ |
| parameter | degrees of freedom ⓘ |
| f(x;k) = 1/(2^{k/2} Γ(k/2)) x^{k/2-1} e^{-x/2} for x>0 ⓘ | |
| relatedTo |
F-distribution
ⓘ
Student's t-distribution ⓘ
linked to:
Student’s t-distribution
gamma distribution ⓘ standard normal distribution ⓘ |
| skewness | √(8/k) ⓘ |
| specialCase | exponential distribution when k = 2 ⓘ |
| support | [0, ∞) ⓘ |
| symbol | χ² ⓘ |
| tailBehavior | heavy right tail for small degrees of freedom ⓘ |
| usedFor |
confidence interval for variance
ⓘ
goodness-of-fit test ⓘ test of homogeneity ⓘ test of independence ⓘ variance test ⓘ |
| usedIn |
analysis of variance
ⓘ
categorical data analysis ⓘ contingency table analysis ⓘ hypothesis testing ⓘ likelihood ratio tests ⓘ maximum likelihood estimation theory ⓘ |
| usedWith |
Pearson's chi-square test
ⓘ
likelihood ratio chi-square test ⓘ |
| variance | 2k (degrees of freedom) ⓘ |
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: chi-square distribution Description of subject: The chi-square distribution is a continuous probability distribution commonly used in statistics to model the sum of squared standard normal variables and to conduct hypothesis tests such as goodness-of-fit and tests of independence.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: chi-square distribution
linked to: chi-square distribution
linked to: chi-square distribution