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Generalized pareto distribution Calculator

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/ Probability Function
/ Pareto distribution

Calculates the probability density function and lower and upper cumulative distribution functions of the generalized pareto distribution.


percentile x
location parameter μ
scale parameter σ
shape parameter ξ

\(\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.
\\
\)

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The hyperlink to [Generalized pareto distribution]: <a href="https://keisan.casio.com/exec/system/15317865995531">Generalized pareto distribution Calculator</a>

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