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gptkbp:instanceOf
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gptkb:organization
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gptkbp:alsoKnownAs
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t-distribution
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gptkbp:category
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continuous probability distribution
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gptkbp:convergesTo
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normal distribution as degrees of freedom increase
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gptkbp:hasCumulativeDistributionFunction
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expressed in terms of the incomplete beta function
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gptkbp:hasMean
|
0
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gptkbp:hasSpecialCase
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gptkb:Pearson_type_VII_distribution
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gptkbp:hasVariance
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n/(n-2) for n>2
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https://www.w3.org/2000/01/rdf-schema#label
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student's t-distribution
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gptkbp:introduced
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gptkb:William_Sealy_Gosset
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gptkbp:introducedIn
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1908
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gptkbp:kurtosis
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greater than normal distribution for small degrees of freedom
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gptkbp:mode
|
0
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gptkbp:namedAfter
|
Student (pseudonym of William Sealy Gosset)
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gptkbp:parameter
|
degrees of freedom
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gptkbp:pdf
|
f(x) = Γ((ν+1)/2) / (√(νπ) Γ(ν/2)) (1 + x²/ν)^(-(ν+1)/2)
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gptkbp:publishedIn
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gptkb:Biometrika
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gptkbp:relatedTo
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gptkb:F-distribution
gptkb:normal_distribution
gptkb:chi-squared_distribution
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gptkbp:skewness
|
0
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gptkbp:supports
|
all real numbers
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gptkbp:symmetry
|
true
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gptkbp:used_in
|
population standard deviation is unknown
sample size is small
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gptkbp:usedFor
|
hypothesis testing
estimating population parameters
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gptkbp:usedIn
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gptkb:t-test
statistics
confidence intervals
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gptkbp:bfsParent
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gptkb:chi-squared_distribution
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gptkbp:bfsLayer
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6
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