(Q3258521)

English

inverse-gamma distribution

distribution of the reciprocal of a variable distributed according to the gamma distribution

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Statements

subclass of

probability distribution

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Inverse-Wishart distribution

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facet of

Bayesian statistics

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image

Inv gamma pdf.svg
600 × 480; 66 KB

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defining formula

f(x;\alpha ,\beta )={\frac {\beta ^{\alpha }}{\Gamma (\alpha )}}(1/x)^{\alpha +1}\exp \left(-\beta /x\right)

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maintained by WikiProject

WikiProject Mathematics

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support of a function

x\in (0,\infty )

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cumulative distribution function

{\frac {\Gamma (\alpha ,\beta /x)}{\Gamma (\alpha )}}

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mean of a probability distribution

{\frac {\beta }{\alpha -1}}

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variance of a probability distribution

{\frac {\beta ^{2}}{(\alpha -1)^{2}(\alpha -2)}}

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skewness

{\frac {4{\sqrt {\alpha -2}}}{\alpha -3}}

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moment-generating function

no value

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Identifiers

1 reference

28 October 2013

Microsoft Academic ID

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1 reference

26 January 2022

https://docs.openalex.org/download-snapshot/snapshot-data-format

(Q3258521)

inverse-gamma distribution

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