dist_gpd: The Generalized Pareto Distribution

In distributional: Vectorised Probability Distributions

The Generalized Pareto Distribution

Description

The GPD distribution function with parameters \code{location} = a, \code{scale} = b and \code{shape} = s is

Usage

dist_gpd(location, scale, shape)

Arguments

location	the location parameter a of the GPD distribution.
scale	the scale parameter b of the GPD distribution.
shape	the shape parameter s of the GPD distribution.

Details

F(x) = 1 - \left(1+s(x-a)/b\right)^{-1/s}

for 1+s(x-a)/b > 0, where b > 0. If s = 0 the distribution is defined by continuity, giving

F(x) = 1 - \exp\left(-\frac{x-a}{b}\right)

The support of the distribution is x \geq a if s \geq 0, and a \leq x \leq a -b/s if s < 0.

The Pickands–Balkema–De Haan theorem states that for a large class of distributions, the tail (above some threshold) can be approximated by a GPD.

See Also

gpd

Examples

dist <- dist_gpd(location = 0, scale = 1, shape = 0)

distributional documentation built on Sept. 17, 2024, 9:11 a.m.