Generalized Pareto {POT}R Documentation

The Generalized Pareto Distribution

Description

Density, distribution function, quantile function and random generation for the GP distribution with location equal to 'loc', scale equal to 'scale' and shape equal to 'shape'.

Usage

rgpd(n, loc = 0, scale = 1, shape = 0)
pgpd(q, loc = 0, scale = 1, shape = 0, lower.tail = TRUE)
qgpd(p, loc = 0, scale = 1, shape = 0, lower.tail = TRUE)
dgpd(x, loc = 0, scale = 1, shape = 0, log = FALSE)

Arguments

x, q vector of quantiles.
p vector of probabilities.
n number of observations.
loc vector of the location parameters.
scale vector of the scale parameters.
shape a numeric of the shape parameter.
lower.tail logical; if TRUE (default), probabilities are P[ X <= x], otherwise, P[X > x].
log logical; if TRUE, probabilities p are given as log(p).

Value

If 'loc', 'scale' and 'shape' are not specified they assume the default values of '0', '1' and '0', respectively.
The GP distribution function for loc = μ, scale = σ and shape = xi is

G(z) = 1 - [ 1 + xi ( z - μ ) / σ ]^(-1/xi)


for 1 + xi ( z - μ ) / σ > 0 and z > μ, where σ > 0. If xi = 0, the distribution is defined by continuity corresponding to the exponential distribution.

Examples

dgpd(0.1)
rgpd(100, 1, 2, 0.2)
qgpd(seq(0.1, 0.9, 0.1), 1, 0.5, -0.2)
pgpd(12.6, 2, 0.5, 0.1)

[Package POT version 1.0-1 Index]