# Gumbel-class

0th

Percentile

##### 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 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.

##### Slots

img

Object of class "Reals".

param

Object of class "GumbelParameter".

r

rgumbel

d

dgumbel

p

pgumbel

q

qgumbel

gaps

(numeric) matrix or NULL

.withArith

logical: used internally to issue warnings as to interpretation of arithmetics

.withSim

logical: used internally to issue warnings as to accuracy

.logExact

logical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function

.lowerExact

logical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function

Symmetry

object of class "DistributionSymmetry"; used internally to avoid unnecessary calculations.

##### Extends

Class "AbscontDistribution", directly. Class "UnivariateDistribution", by class "AbscontDistribution". Class "Distribution", by class "AbscontDistribution".

##### Methods

initialize

signature(.Object = "Gumbel"): initialize method.

loc

signature(object = "Gumbel"): wrapped access method for slot loc of slot param.

scale

signature(x = "Gumbel"): wrapped access method for slot scale of slot param.

loc<-

signature(object = "Gumbel"): wrapped replace method for slot loc of slot param.

scale<-

signature(x = "Gumbel"): wrapped replace method for slot scale of slot param.

+

signature(e1 = "Gumbel", e2 = "numeric"): result again of class "Gumbel"; exact.

*

signature(e1 = "Gumbel", e2 = "numeric"): result again of class "Gumbel"; exact.

E

signature(object = "Gumbel", fun = "missing", cond = "missing"): exact evaluation of expectation using explicit expressions.

var

signature(x = "Gumbel"): exact evaluation of expectation using explicit expressions.

skewness

signature(x = "Gumbel"): exact evaluation of expectation using explicit expressions.

kurtosis

signature(x = "Gumbel"): exact evaluation of expectation using explicit expressions.

median

signature(x = "Gumbel"): exact evaluation of expectation using explicit expressions.

IQR

signature(x = "Gumbel"): exact evaluation of expectation using explicit expressions.

liesInSupport

signature(object = "Gumbel", x = "numeric"): checks if x lies in the support of the respective distribution.

##### References

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

rgumbel, AbscontDistribution-class

##### Aliases
• Gumbel-class
• initialize,Gumbel-method
• loc,Gumbel-method
• loc<-,Gumbel-method
• scale,Gumbel-method
• scale<-,Gumbel-method
• +,Gumbel,numeric-method
• *,Gumbel,numeric-method
• liesInSupport,Gumbel,numeric-method
##### Examples
# NOT RUN {
(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 RobExtremes, version 1.2.0, License: LGPL-3

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