dGEV: The Generalized Extreme Value Distribution

In ExtremalDep: Extremal Dependence Models

The Generalized Extreme Value Distribution

Description

Density, distribution and quantile function for the Generalized Extreme Value (GEV) distribution.

Usage

dGEV(x, loc, scale, shape, log = FALSE)
pGEV(q, loc, scale, shape, lower.tail = TRUE)
qGEV(p, loc, scale, shape)

Arguments

x, q	Vector of quantiles.
p	Vector of probabilities.
loc	Vector of locations.
scale	Vector of scales.
shape	Vector of shapes.
log	Logical; if TRUE, returns the log density.
lower.tail	Logical; if TRUE, probabilities are P(X \leq x), otherwise P(X > x).

Details

The GEV distribution has density

f(x; \mu, \sigma, \xi) = \exp \left\{ -\left[ 1 + \xi \left( \frac{x-\mu}{\sigma} \right)\right]_+^{-1/\xi}\right\}

Value

Density (dGEV), distribution function (pGEV) and quantile function (qGEV) from the Generalized Extreme Value distribution with given location, scale and shape.

Author(s)

Simone Padoan, [e-mail], https://faculty.unibocconi.it/simonepadoan/; Boris Beranger, [e-mail], https://www.borisberanger.com.

See Also

fGEV

Examples

# Densities
dGEV(x = 1, loc = 1, scale = 1, shape = 1)
dGEV(x = c(0.2, 0.5), loc = 1, scale = 1, shape = c(0, 0.3))

# Probabilities
pGEV(q = 1, loc = 1, scale = 1, shape = 1, lower.tail = FALSE)
pGEV(q = c(0.2, 0.5), loc = 1, scale = 1, shape = c(0, 0.3))

# Quantiles
qGEV(p = 0.5, loc = 1, scale = 1, shape = 1)
qGEV(p = c(0.2, 0.5), loc = 1, scale = 1, shape = c(0, 0.3))

ExtremalDep documentation built on Aug. 21, 2025, 5:57 p.m.