# GUMBEL: Gumbel Distribution (for maxima) In FAdist: Distributions that are Sometimes Used in Hydrology

 GUMBEL R Documentation

## 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')