ExtremalDep (version 0.0.4-4)

dGEV: 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)

Value

density (dGEV), distribution function (pGEV) and quantile function (qGEV) from the Generalized Extreme Value distirbution with given

location, scale and shape.

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

loc

vector of locations.

scale

vector of scales.

shape

vector of shapes.

log

A logical value; if TRUE returns the log density.

lower.tail

A logical value; if TRUE probabilities are \(P\left(X \leq x \right)\), otherwise \(P\left(X > x \right)\).

Author

Simone Padoan, , https://faculty.unibocconi.it/simonepadoan/; Boris Beranger, https://www.borisberanger.com;

Details

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

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))