evd: gpd – R documentation

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gpd

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.

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

Functions for Extreme Value Distributions

v2.3-3

GPL-3

Authors

Alec Stephenson. Function fbvpot by Chris Ferro.

Initial release

2018-04-25

gpd