pdfGenPareto#

Purpose#

Computes the probability density function for the Generalized Pareto distribution.

Format#

y = pdfGenPareto(x, a, sigma, k)#

Parameters:

x (NxK matrix, Nx1 vector or scalar.) – data
a (NxK matrix, Nx1 vector or scalar) – Location parameter, ExE conformable with x.
sigma (NxK matrix, Nx1 vector or scalar) – Scale parameter, ExE conformable with x. sigma must be greater than 0.
k (NxK matrix, Nx1 vector or scalar) – Shape parameter, ExE conformable with x.

Returns:

p (NxK matrix, Nx1 vector or scalar) – the probability density function for the Generalized Pareto distribution for the elements in x.

Remarks#

The probability density function for the Generalized Pareto distribution is defined as

\[\begin{split}f(x)= \begin{cases} \frac{1}{\sigma}\big(1 + k \frac{x-\mu}{\sigma} \big)^{-1 - 1/k},& k\neq 0\\ \frac{1}{\sigma}exp(\frac{x-\mu}{\sigma}), & k = 0 \end{cases}\end{split}\]