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).

Note

This class is based on the code provided by the package evd.

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
• extreme value distribution
• absolutely continuous distribution
• S4 distribution class

References

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

See Also

rgumbel, AbscontDistribution-class

Aliases

• Gumbel-class
• initialize,Gumbel-method
• loc,Gumbel-method
• loc<-,Gumbel-method
• scale,Gumbel-method
• scale<-,Gumbel-method

Examples

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