# Gumbel-class

##### Gumbel distribution

The Gumbel cumulative distribution function with
location parameter `loc`

$= \mu$ and scale
parameter `scale`

$= \sigma$ is
$$F(x) = \exp(-\exp[-(x-\mu)/\sigma])$$
for all real x, where $\sigma > 0$;
c.f. `rgumbel`

. This distribution is also known as
extreme value distribution of type I; confer Chapter~22 of
Johnson et al. (1995).

- Keywords
- distribution

##### Note

This class is based on the code provided by the package

##### Objects from the Class

Objects can be created by calls of the form `new("Gumbel", loc, scale)`

.
More frequently they are created via the generating function
`Gumbel`

.

##### Extends

Class `"AbscontDistribution"`

, directly.
Class `"UnivariateDistribution"`

, by class `"AbscontDistribution"`

.
Class `"Distribution"`

, by class `"AbscontDistribution"`

.

##### concept

Gumbel

##### References

Johnson et al. (1995) *Continuous Univariate Distributions. Vol. 2. 2nd ed.*
New York: Wiley.

##### See Also

##### Examples

```
(G1 <- new("Gumbel", loc = 1, scale = 2))
plot(G1)
loc(G1)
scale(G1)
loc(G1) <- -1
scale(G1) <- 2
plot(G1)
```

*Documentation reproduced from package distrEx, version 0.4-2, License: GPL (version 2 or later)*