Student’s t-distribution

E596524

location-scale family probability distribution

Student’s t-distribution is a continuous probability distribution used primarily to estimate population means and conduct hypothesis tests when sample sizes are small and population variance is unknown.

Try in SPARQL Jump to: Surface forms Disambiguation Statements Elicitation Referenced by

All labels observed (6)

Label	Occurrences
Student's t-distribution	4
Student t-distribution	2
Student’s t-distribution canonical	2
t-distribution	2
Student's t-test	1
t-statistic	1

How this entity was disambiguated

This entity first appeared as the object of triple T6482583 — 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: Student’s t-distribution
Context triple: [Gamma function, appearsIn, Student’s t-distribution]

A. 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.
B. 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.
C. 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.
D. Tukey's honestly significant difference test
Tukey's honestly significant difference test is a statistical post-hoc procedure used to determine which specific group means differ after an ANOVA indicates a significant overall effect.
E. Tukey's biweight
Tukey's biweight is a robust statistical estimator that downweights outliers to provide resistant measures of central tendency or regression fits.
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: Student’s t-distribution
Target entity description: Student’s t-distribution is a continuous probability distribution used primarily to estimate population means and conduct hypothesis tests when sample sizes are small and population variance is unknown.

A. 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.
B. 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.
C. 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.
D. Tukey's honestly significant difference test
Tukey's honestly significant difference test is a statistical post-hoc procedure used to determine which specific group means differ after an ANOVA indicates a significant overall effect.
E. Tukey's biweight
Tukey's biweight is a robust statistical estimator that downweights outliers to provide resistant measures of central tendency or regression fits.
F. None of above. chosen

Statements (44)

Predicate	Object
instanceOf	location-scale family ⓘ probability distribution ⓘ
alsoKnownAs	Student t-distribution ⓘ linked to: Student’s t-distribution t-distribution ⓘ linked to: Student’s t-distribution
appearsIn	Bayesian posterior for mean with unknown variance under conjugate priors ⓘ
arisesFrom	ratio of standard normal variable to square root of scaled chi-square variable ⓘ
belongsTo	location-scale t-family ⓘ
convergesTo	standard normal distribution as degrees of freedom go to infinity ⓘ
cumulativeDistributionFunction	expressible via incomplete beta function ⓘ
definedBy	degrees of freedom parameter ν>0 ⓘ
familyMemberOf	elliptical distributions ⓘ
hasHeavierTailsThan	normal distribution ⓘ
introducedBy	William Sealy Gosset ⓘ
introducedInYear	1908 ⓘ
introducedUnderPseudonym	Student ⓘ
isScaleMixtureOf	normal distributions ⓘ
isSymmetricAbout	0 ⓘ
kurtosisExcess	6/(ν-4) for ν>4 ⓘ
limitingCase	standard normal distribution as ν→∞ ⓘ
mean	0 for degrees of freedom greater than 1 ⓘ
median	0 ⓘ
mode	0 ⓘ
namedAfter	William Sealy Gosset ⓘ
parameter	degrees of freedom ⓘ
probabilityDensityFunction	f(x)=Γ((ν+1)/2)/(√(νπ)Γ(ν/2))·(1+x²/ν)^(-(ν+1)/2) ⓘ
relatedDistribution	Cauchy distribution ⓘ F-distribution ⓘ chi-square distribution ⓘ
skewness	0 for ν>3 ⓘ
specialCase	Cauchy distribution when ν=1 ⓘ
sufficientStatisticContext	sample mean with unknown variance in normal model ⓘ
support	all real numbers ⓘ
tailBehavior	polynomial decay ⓘ
usedFor	confidence intervals for means ⓘ inference on population mean with unknown variance ⓘ one-sample t-test ⓘ paired t-test ⓘ regression coefficient inference ⓘ two-sample t-test ⓘ
usedWhen	population variance is unknown ⓘ sample size is small ⓘ
variance	infinite for 1<ν≤2 ⓘ undefined for ν≤1 ⓘ ν/(ν-2) for degrees of freedom greater than 2 ⓘ

How these facts were elicited

Referenced by (12)

Full triples — surface form annotated when it differs from this entity's canonical label.

Gamma function → appearsIn → Student’s t-distribution ⓘ

Hotelling’s T-squared distribution → isGeneralizationOf → Student’s t-distribution ⓘ

F-distribution → relatedDistribution → Student's t-distribution ⓘ