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

## 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

 ```1 2 3 4``` ```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

 ```1 2 3``` ```x <- rgumbel(1000,3,100) hist(x,freq=FALSE,col='gray',border='white') curve(dgumbel(x,3,100),add=TRUE,col='red4',lwd=2) ```

### Example output

```
```

FAdist documentation built on April 17, 2020, 1:24 a.m.