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Inverse-gamma distribution : ウィキペディア英語版
Inverse-gamma distribution

\! for \alpha > 3|
kurtosis =\frac\! for \alpha > 4|
entropy =\alpha\!+\!\ln(\beta\Gamma(\alpha))\!-\!(1\!+\!\alpha)\Psi(\alpha)|
mgf =Does not exist.|
char =\frac}}K_\left(\sqrt\right)|
}}
In probability theory and statistics, the inverse gamma distribution is a two-parameter family of continuous probability distributions on the positive real line, which is the distribution of the reciprocal of a variable distributed according to the gamma distribution. Perhaps the chief use of the inverse gamma distribution is in Bayesian statistics, where the distribution arises as the marginal posterior distribution for the unknown variance of a normal distribution if an uninformative prior is used; and as an analytically tractable conjugate prior if an informative prior is required.
However, it is common among Bayesians to consider an alternative parametrization of the normal distribution in terms of the precision, defined as the reciprocal of the variance, which allows the gamma distribution to be used directly as a conjugate prior. Other Bayesians prefer to parametrize the inverse gamma distribution differently, as a scaled inverse chi-squared distribution.
==Characterization==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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