Chi-squared distribution (λ=0)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	Probability distribution
gptkbp:alsoKnownAs	Central chi-squared distribution
gptkbp:cumulativeDistributionFunction	γ(k/2, x/2)/Γ(k/2)
gptkbp:domain	gptkb:Probability_theory Statistics
gptkbp:firstDescribed	1900
gptkbp:hasSpecialCase	gptkb:Gamma_distribution Noncentral chi-squared distribution (λ=0)
https://www.w3.org/2000/01/rdf-schema#label	Chi-squared distribution (λ=0)
gptkbp:kurtosis	12/k
gptkbp:meaning	k
gptkbp:mode	max(k-2, 0)
gptkbp:namedAfter	gptkb:Karl_Pearson
gptkbp:origin	Sum of squares of k independent standard normal random variables
gptkbp:parameter	Degrees of freedom (k) k (integer > 0)
gptkbp:pdf	(1/(2^{k/2}Γ(k/2))) x^{k/2-1} e^{-x/2}
gptkbp:relatedTo	gptkb:F-distribution gptkb:Student's_t-distribution gptkb:Noncentral_chi-squared_distribution gptkb:Gamma_distribution gptkb:Normal_distribution
gptkbp:skewness	sqrt(8/k)
gptkbp:supports	x ≥ 0
gptkbp:usedIn	Confidence interval estimation Goodness-of-fit tests Statistical hypothesis testing
gptkbp:variant	2k
gptkbp:bfsParent	gptkb:Noncentral_chi-squared_distribution
gptkbp:bfsLayer	7