Inverse gamma distribution

GPTKB entity

Predicate	Object
gptkbp:instanceOf	Probability distribution
gptkbp:application	gptkb:Hierarchical_Bayesian_models Variance component modeling
gptkbp:category	Continuous distribution
gptkbp:conjugatePriorFor	variance of normal distribution
gptkbp:cumulativeDistributionFunction	Γ(α, β/x) / Γ(α)
gptkbp:definedIn	reciprocal of gamma-distributed variable
https://www.w3.org/2000/01/rdf-schema#label	Inverse gamma distribution
gptkbp:kurtosis	6(5α-11)/((α-3)(α-4)), for α > 4
gptkbp:meaning	β / (α - 1), for α > 1
gptkbp:mode	β / (α + 1)
gptkbp:notation	Inv-Gamma(α, β)
gptkbp:parameter	alpha (shape parameter) beta (scale parameter)
gptkbp:probabilityDensityFunction	(β^α / Γ(α)) x^(-α-1) exp(-β/x)
gptkbp:relatedTo	gptkb:Gamma_distribution gptkb:Inverse_chi-squared_distribution
gptkbp:skewness	4√(α-2)/ (α-3), for α > 3
gptkbp:supports	x > 0
gptkbp:usedIn	Bayesian statistics
gptkbp:variant	β^2 / ((α - 1)^2 (α - 2)), for α > 2
gptkbp:bfsParent	gptkb:Gamma_distribution gptkb:Pearson_Type_V
gptkbp:bfsLayer	6