Generalized Pareto distribution

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Generalized Pareto distribution is defined by three parameters denoted k , \sigma  and \theta . The probability density function depends from the value of the parameters, several cases have to be distinguished.

  • k > 0

The support of the distribution is [\theta, \infty]. The probability density function is

f(x) = \left(\frac{1}{\sigma}\right)  \left(1 + k \frac{x- \theta}{\sigma} \right) ^{-1- \frac{1}{k}}


  • k < 0

The support of the distribution is [ -\infty, \theta]. The probability density function is

f(x) = \left(\frac{1}{\sigma}\right)  \left(1 + k \frac{x- \theta}{\sigma} \right) ^{-1- \frac{1}{k}}
  • k = 0 ,

The support of the distribution is [ -\infty, \infty]. The probability density function is:

f(x) = \left(\frac{1}{\sigma}\right) exp  \left( \frac{x- \theta}{\sigma} \right)


Gppdf.png
Gpcdf.png

External link

Generalized Pareto distribution