# 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:

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