gumbel: Gumbel distribution

In RTMBdist: Distributions Compatible with Automatic Differentiation by 'RTMB'

Gumbel distribution

Description

Density, distribution function, quantile function, and random generation for the Gumbel distribution.

Usage

dgumbel(x, location = 0, scale = 1, log = FALSE)

pgumbel(q, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)

qgumbel(p, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)

rgumbel(n, location = 0, scale = 1)

Arguments

x, q	vector of quantiles
location	location parameter
scale	scale parameter, must be positive.
log, log.p	logical; if TRUE, probabilities/ densities p are returned as \log(p).
lower.tail	logical; if TRUE, probabilities are P[X \le x], otherwise, P[X > x].
p	vector of probabilities
n	number of random values to return

Details

This implementation of dgumbel allows for automatic differentiation with RTMB.

f(x;\,\mu,\sigma) = \frac{1}{\sigma}\exp\!\bigl(-(z + e^{-z})\bigr), \quad z = \frac{x-\mu}{\sigma}.

Value

dgumbel gives the density, pgumbel gives the distribution function, qgumbel gives the quantile function, and rgumbel generates random deviates.

See Also

gev, frechet, gpd

Examples

x <- rgumbel(1, 0.5, 2)
d <- dgumbel(x, 0.5, 2)
p <- pgumbel(x, 0.5, 2)
q <- qgumbel(p, 0.5, 2)

RTMBdist documentation built on Oct. 31, 2026, 5:07 p.m.