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

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

Examples#

// Data points
x = { 0.5, 1, 2, 3 };

// Generalized Pareto PDF with location = 0, scale = 1, shape = 0.5
p = pdfGenPareto(x, 0, 1, 0.5);
print p;

After the code above, p is equal to:

 0.51200000
 0.29629630
 0.12500000
0.064000000

See also

Functions cdfGenPareto()

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