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gptkbp:instanceOf
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Probability distribution
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gptkbp:asymptoticTo
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Normal distribution (for large k)
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gptkbp:category
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gptkb:Probability_theory
Statistical distributions
Continuous distributions
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gptkbp:characteristic
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(1-2it)^{-k/2}
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gptkbp:continuity
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true
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gptkbp:cumulativeDistributionFunction
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P(x; k) = γ(k/2, x/2)/Γ(k/2)
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gptkbp:entropy
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Depends on k, involves digamma and gamma functions
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gptkbp:firstDescribed
|
1900
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gptkbp:hasSpecialCase
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gptkb:Gamma_distribution
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https://www.w3.org/2000/01/rdf-schema#label
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Chi-squared distribution
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gptkbp:isRightSkewed
|
true
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gptkbp:isUnimodal
|
true
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gptkbp:kurtosis
|
12/k
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gptkbp:meaning
|
k (degrees of freedom)
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gptkbp:mode
|
max(k-2, 0)
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gptkbp:momentGeneratingFunction
|
(1-2t)^{-k/2}, t < 1/2
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gptkbp:namedAfter
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gptkb:Karl_Pearson
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gptkbp:notation
|
χ²(k)
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gptkbp:parameter
|
Degrees of freedom
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gptkbp:pdf
|
f(x; k) = (1/(2^{k/2} Γ(k/2))) x^{k/2-1} e^{-x/2}
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gptkbp:relatedTo
|
gptkb:F-distribution
gptkb:Student's_t-distribution
gptkb:Noncentral_chi-squared_distribution
gptkb:Gamma_distribution
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gptkbp:skewness
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sqrt(8/k)
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gptkbp:sumOf
|
Squares of k independent standard normal random variables
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gptkbp:supports
|
[0, ∞)
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gptkbp:usedFor
|
Model fit assessment
Testing independence in contingency tables
Variance estimation
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gptkbp:usedIn
|
gptkb:Hypothesis_testing
Statistics
Confidence interval estimation
Goodness-of-fit tests
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gptkbp:variant
|
2k (degrees of freedom)
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gptkbp:bfsParent
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gptkb:F-distribution
gptkb:Student's_t-distribution
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gptkbp:bfsLayer
|
5
|