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Generalized Pareto distribution : ウィキペディア英語版
Generalized Pareto distribution

In statistics, the generalized Pareto distribution (GPD) is a family of continuous probability distributions. It is often used to model the tails of another distribution. It is specified by three parameters: location \mu, scale \sigma, and shape \xi. Sometimes it is specified by only scale and shape and sometimes only by its shape parameter. Some references give the shape parameter as \kappa = - \xi \,.
==Definition==
The standard cumulative distribution function (cdf) of the GPD is defined by
: F_(z) = \begin
1 - \left(1+ \xi z\right)^ & \text\xi \neq 0, \\
1 - e^ & \text\xi = 0.
\end

where the support is z \geq 0 for \xi \geq 0 and 0 \leq z \leq - 1 /\xi for \xi < 0.
: f_(z) = \begin
(\xi z+1)^} & \text\xi \neq 0, \\
e^ & \text\xi = 0.
\end


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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