gpd: The Generalized Pareto Distribution

In evd: Functions for Extreme Value Distributions

The Generalized Pareto Distribution

Description

Density function, distribution function, quantile function and random generation for the generalized Pareto distribution (GPD) with location, scale and shape parameters.

Usage

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

Arguments

x, q	Vector of quantiles.
p	Vector of probabilities.
n	Number of observations.
loc, scale, shape	Location, scale and shape parameters; the shape argument cannot be a vector (must have length one).
log	Logical; if TRUE, the log density is returned.
lower.tail	Logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]

Details

The generalized Pareto distribution function (Pickands, 1975) with parameters \code{loc} = a, \code{scale} = b and \code{shape} = s is

G(z) = 1 - \{1+s(z-a)/b\}^{-1/s}

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

Value

dgpd gives the density function, pgpd gives the distribution function, qgpd gives the quantile function, and rgpd generates random deviates.

References

Pickands, J. (1975) Statistical inference using extreme order statistics. Annals of Statistics, 3, 119–131.

See Also

fpot, rgev

Examples

dgpd(2:4, 1, 0.5, 0.8)
pgpd(2:4, 1, 0.5, 0.8)
qgpd(seq(0.9, 0.6, -0.1), 2, 0.5, 0.8)
rgpd(6, 1, 0.5, 0.8)
p <- (1:9)/10
pgpd(qgpd(p, 1, 2, 0.8), 1, 2, 0.8)
## [1] 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

evd documentation built on Sept. 21, 2024, 9:06 a.m.