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

In probability theory and statistics, the normal-exponential-gamma distribution (sometimes called the NEG distribution) is a three-parameter family of continuous probability distributions. It has a location parameter \mu, scale parameter \theta and a shape parameter k .
==Probability density function==
The probability density function (pdf) of the normal-exponential-gamma distribution is proportional to
:f(x;\mu, k,\theta) \propto \exp\right)}D_\left(\frac\right)\,\!,
where ''D'' is a parabolic cylinder function.〔http://www.newton.ac.uk/programmes/SCB/seminars/121416154.html 〕
As for the Laplace distribution, the pdf of the NEG distribution can be expressed as a mixture of normal distributions,
:f(x;\mu, k,\theta)=\int_0^\infty\int_0^\infty\ \mathrm(x| \mu, \sigma^2)\mathrm(\sigma^2|\psi)\mathrm(\psi|k, 1/\theta^2) \, d\sigma^2 \, d\psi,
where, in this notation, the distribution-names should be interpreted as meaning the density functions of those distributions.

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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