Gumbel: The Gumbel Distribution

In RcmdrMisc: R Commander Miscellaneous Functions

The Gumbel Distribution

Description

The Gumbel Distribution

Usage

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

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

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

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

Arguments

x	vector of values of the variable.
location	location parameter (default 0); potentially a vector.
scale	scale parameter (default 1); potentially a vector.
q	vector of quantiles.
lower.tail	logical; if TRUE (the default) probabilities and quantiles correspond to P(X \le x), if FALSE to P(X > x).
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.

Details

Density, distribution function, quantile function and random generation for the Gumbel distribution with specified location and scale parameters.

Author(s)

John Fox

References

See https://en.wikipedia.org/wiki/Gumbel_distribution for details of the Gumbel distribution.

Examples

x <- 100 + 5*c(-Inf, -1, 0, 1, 2, 3, Inf, NA)
dgumbel(x, 100, 5)
pgumbel(x, 100, 5)
p <- c(0, .25, .5, .75, 1, NA)
qgumbel(p, 100, 5)
summary(rgumbel(1e5, 100, 5))

RcmdrMisc documentation built on Jan. 8, 2026, 9:06 a.m.