GEV-class {RobExtremes}

Generalized EV distribution

Description

[borrowed from evd]: The GEV distribution function with parameters loc = a, scale = b, shape = s is

G(x) = exp[-{1+s(z-a)/b}^(-1/s)]

for 1+s(z-a)/b > 0, where b > 0. If s = 0 the distribution is defined by continuity and gives the Gumbel distribution. If 1+s(z-a)/b \leq 0, the value z is either greater than the upper end point (if s < 0), or less than the lower end point (if s > 0).

Objects from the Class

Objects can be created by calls of the form new("GEV", loc, scale,shape). More frequently they are created via the generating function GEV.

Slots

img

Object of class "Reals".

param

Object of class "GEVParameter".

r

rgpd

d

dgpd

p

pgpd, but vectorized and with special treatment of arguments lower.tail and log.p

q

qgpd, but vectorized and with special treatment of arguments lower.tail and log.p

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

Extends

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

Methods

initialize

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

shape

signature(object = "GEV"): wrapped access method for slot shape of slot param.

loc

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

location

signature(object = "GEV"): alias to loc, to support argument naming of package VGAM.

scale

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

shape<-

signature(object = "GEV"): wrapped replace method for slot shape of slot param.

loc<-

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

location<-

signature(object = "GEV"): alias to loc<-, to support argument naming of package VGAM.

scale<-

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

+

signature(e1 = "GEV", e2 = "numeric"): exact method for this transformation — stays within this class.

*

signature(e1 = "GEV", e2 = "numeric"): exact method for this transformation — stays within this class if e2>0.

E

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

var

signature(signature(x = "GEV"): exact evaluation using explicit expressions.

median

signature(signature(x = "GEV"): exact evaluation using explicit expressions.

IQR

signature(signature(x = "GEV"): exact evaluation using explicit expressions.

skewness

signature(signature(x = "GEV"): exact evaluation using explicit expressions.

kurtosis

signature(signature(x = "GEV"): exact evaluation using explicit expressions.

liesInSupport

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

Note

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

Author(s)

Nataliya Horbenko [e-mail]

References

Pickands, J. (1975) Statistical inference using extreme order statistics. _Annals of Statistics_, *3*, 119-131.

See Also

dgpd, AbscontDistribution-class

Examples

(P1 <- new("GEV", loc = 0, scale = 1,shape = 0))
plot(P1)
shape(P1)
loc(P1)
scale(P1) <- 4
loc(P1) <- 2
shape(P1) <- -1 # may be negative!
plot(P1)