# 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')