ROptEstOld (version 1.2.0)

Gumbel-class: Gumbel distribution

Description

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).

Usage

E(object, fun, cond, ...)
# S4 method for Gumbel,missing,missing
E(object, low = NULL, upp = NULL, ...)
var(x, ...)
# S4 method for Gumbel
var(x, ...)
skewness(x, ...)
# S4 method for Gumbel
skewness(x, ...)
kurtosis(x, ...)
# S4 method for Gumbel
kurtosis(x, ...)

Arguments

object

object of class "Distribution"

fun

if missing the (conditional) expectation is computed else the (conditional) expection of fun is computed.

cond

if not missing the conditional expectation given cond is computed.

low

lower bound of integration range.

upp

upper bound of integration range.

x

object of class "UnivariateDistribution"

…

additional arguments to fun

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.

References

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

See Also

rgumbel, AbscontDistribution-class

Examples

# NOT RUN {
(G1 <- new("Gumbel", loc = 1, scale = 2))
plot(G1)
loc(G1)
scale(G1)
loc(G1) <- -1
scale(G1) <- 2
plot(G1)
# }