GUMBEL: Gumbel Distribution (for maxima)

In FAdist: Distributions that are Sometimes Used in Hydrology

Gumbel Distribution (for maxima)

Description

Density, distribution function, quantile function and random generation for the Gumbel distribution (for maxima) with scale and location parameters equal to scale and location, respectively.

Usage

dgumbel(x,scale=1,location=0,log=FALSE)
pgumbel(q,scale=1,location=0,lower.tail=TRUE,log.p=FALSE)
qgumbel(p,scale=1,location=0,lower.tail=TRUE,log.p=FALSE)
rgumbel(n,scale=1,location=0)

Arguments

x,q	vector of quantiles.
p	vector of probabilities.
n	number of observations.
scale	scale parameter.
location	location parameter.
log,log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X <= x],otherwise, P[X > x].

Details

If X is a random variable distributed according to a Gumbel distribution, it has density
f(x) = 1/scale*exp(-(x-location)/scale-exp(-(x-location)/scale))

Value

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

References

Coles, S. (2001) An introduction to statistical modeling of extreme values. Springer

Examples

x <- rgumbel(1000,3,100)
hist(x,freq=FALSE,col='gray',border='white')
curve(dgumbel(x,3,100),add=TRUE,col='red4',lwd=2)

FAdist documentation built on March 18, 2022, 5:24 p.m.