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Generalized pareto distribution Calculator

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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

$\normal Generalized\ Pareto\ distribution\\[10]<br />(1)\ probability\ density\\<br />\hspace{30}f(x,\mu,\sigma,\xi)= \left\{ \large \frac{1}{\sigma} \left\{ 1 + \frac{\xi (x- \mu )}{\sigma} \right\}^{\small \left\( - \frac{1}{\xi}-1 \right\)} \hspace{30} {\small \xi \not= 0 } \\<br />\frac{1}{\sigma} \exp \left\{ - \frac{(x- \mu )}{\sigma} \right\} \hspace{65} {\small \xi = 0 } \right. \\<br /><br />(2)\ lower\ cumulative\ distribution\\<br />\hspace{30}P(x,\mu,\sigma,\xi)= \left\{ \large 1- \left\{ 1 + \frac{\xi (x- \mu )}{\sigma} \right\}^{\small - \frac{1}{\xi}} \hspace{30} {\small \xi \not= 0 } \\<br />1 - \exp \left\( - \frac{x- \mu}{\sigma} \right\) \hspace{50} {\small \xi = 0 } \right. \\<br /><br />(3)\ upper\ cumulative\ distribution\\<br />\hspace{30}Q(x,\mu,\sigma,\xi) = \left\{ \large \left\{ 1 + \frac{\xi (x- \mu )}{\sigma} \right\}^{\small - \frac{1}{\xi}} \hspace{30} {\small \xi \not= 0 } \\<br />\exp \left\( - \frac{x- \mu}{\sigma} \right\) \hspace{50} {\small \xi = 0 } \right. \\<br />\\$

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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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