\(\normalsize Generalized\ Pareto\ distribution\\
(1)\ probability\ density\\
\hspace{30px}f(x,\mu,\sigma,\xi)=
\left\{
\begin{array}{l}
\large \frac{1}{\sigma} \left\{ 1 + \frac{\xi (x- \mu )}{\sigma} \right\}^{\small \left( - \frac{1}{\xi}-1 \right)} \hspace{30px} {\small \xi \not= 0 } \\
\frac{1}{\sigma} \exp \left\{ - \frac{(x- \mu )}{\sigma} \right\} \hspace{65px} {\small \xi = 0 }
\end{array}
\right.
\\
(2)\ lower\ cumulative\ distribution\\
\hspace{30px}P(x,\mu,\sigma,\xi)=
\left\{
\begin{array}{l}
\large 1- \left\{ 1 + \frac{\xi (x- \mu )}{\sigma} \right\}^{\small - \frac{1}{\xi}} \hspace{30px} {\small \xi \not= 0 } \\
1 - \exp \left( - \frac{x- \mu}{\sigma} \right) \hspace{50px} {\small \xi = 0 }
\end{array}
\right.
\\
(3)\ upper\ cumulative\ distribution\\
\hspace{30px}Q(x,\mu,\sigma,\xi)=
\left\{
\begin{array}{l}
\large \left\{ 1 + \frac{\xi (x- \mu )}{\sigma} \right\}^{\small - \frac{1}{\xi}} \hspace{30px} {\small \xi \not= 0 } \\
\exp \left( - \frac{x- \mu}{\sigma} \right) \hspace{50px} {\small \xi = 0 }
\end{array}
\right.
\\
\) |
|
ゲストさん
ブックマーク
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