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 Statements Referenced by

Observed surface forms (1)

Surface form	Occurrences
Student's t-distribution	2

Statements (44)

Predicate	Object
instanceOf	location-scale family ⓘ probability distribution ⓘ
alsoKnownAs	Student t-distribution NERFINISHED ⓘ t-distribution NERFINISHED ⓘ
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 NERFINISHED ⓘ
introducedInYear	1908 ⓘ
introducedUnderPseudonym	Student NERFINISHED ⓘ
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 NERFINISHED ⓘ
parameter	degrees of freedom ⓘ
probabilityDensityFunction	f(x)=Γ((ν+1)/2)/(√(νπ)Γ(ν/2))·(1+x²/ν)^(-(ν+1)/2) ⓘ
relatedDistribution	Cauchy distribution NERFINISHED ⓘ F-distribution NERFINISHED ⓘ 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 ⓘ

Referenced by (4)

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 ⓘ

this entity surface form: Student's t-distribution

Cauchy distribution → isSpecialCaseOf → Student’s t-distribution ⓘ

this entity surface form: Student's t-distribution