cdfGenPareto#

Purpose#

Computes the cumulative distribution function for the Generalized Pareto distribution.

Format#

p = cdfGenPareto(x, loc, scale, shape)#

Parameters:

x (NxK matrix, Nx1 vector or scalar) – Values at which to evaluate the Generalized Pareto cdf. \(x > 0\).
loc (NxK matrix, Nx1 vector or scalar) – Location parameter, ExE conformable with x.
scale (NxK matrix, Nx1 vector or scalar) – Scale parameter, ExE conformable with x. \(scale > 0\).
shape (NxK matrix, Nx1 vector or scalar) – Shape parameter, ExE conformable with x.

Returns:

p (NxK matrix, Nx1 vector or scalar) – Each element in p isthe Generalized Pareto cdf evaluated at the corresponding element in x.

Examples#

// Set location parameter
loc = 0;

// Set scale parameter
scale = 2;

// Set shape parameter
shape = 5;

p = cdfGenPareto(3, loc, scale, shape);

After the above code, P is equal to

0.3482

Remarks#

The cumulative distribution function for the Generalized Pareto distribution is defined as:

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