RcmdrMisc (version 2.9-1)

Gumbel: The Gumbel Distribution

Description

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

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, q

vector of quantiles (values of the variable).

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

location

location parameter (default 0); potentially a vector.

scale

scale parameter (default 1); potentially a vector.

lower.tail

logical; if TRUE (the default) probabilities and quantiles correspond to \(P(X \le x)\), if FALSE to \(P(X > x)\).

Author

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))