ExtremalDep (version 1.0.0)

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 distribution 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

Logical; if TRUE, returns the log density.

lower.tail

Logical; if TRUE, probabilities are \(P(X \leq x)\), otherwise \(P(X > x)\).

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))