GEV-class: 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 $s > 0$).

Arguments

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.

Author

Nataliya Horbenko nhorbenko@gmail.com

References

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

Examples

Run this code

(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)

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