# var

0th

Percentile

##### Generic Functions for the Computation of Functionals

Generic functions for the computation of functionals on distributions.

Keywords
methods, distribution
##### Usage
IQR(x, ...)# S4 method for Gumbel
IQR(x)
# S4 method for GEV
IQR(x)
# S4 method for GPareto
IQR(x)
# S4 method for Pareto
IQR(x)median(x, ...)# S4 method for Gumbel
median(x)
# S4 method for GEV
median(x)
# S4 method for GPareto
median(x)
# S4 method for Pareto
median(x)var(x, ...)# S4 method for Gumbel
var(x, ...)
# S4 method for GEV
var(x, ...)
# S4 method for GPareto
var(x, ...)
# S4 method for Pareto
var(x, ...)skewness(x, ...)
# S4 method for Gumbel
skewness(x, ...)
# S4 method for GEV
skewness(x, ...)
# S4 method for GPareto
skewness(x, ...)
# S4 method for Pareto
skewness(x, ...)kurtosis(x, ...)
# S4 method for Gumbel
kurtosis(x, ...)
# S4 method for GEV
kurtosis(x, ...)
# S4 method for GPareto
kurtosis(x, ...)
# S4 method for Pareto
kurtosis(x, ...)Sn(x, ...)
# S4 method for ANY
Sn(x,  ...)
# S4 method for UnivariateDistribution
Sn(x, low = 0, upp = 1.01, accuracy = 1000, ...)
# S4 method for DiscreteDistribution
Sn(x,  ...)
# S4 method for AffLinDistribution
Sn(x,  ...)
# S4 method for Norm
Sn(x,  ...)
# S4 method for GPareto
Sn(x,  ...)
# S4 method for Pareto
Sn(x,  ...)
# S4 method for GEV
Sn(x,  ...)
Sn(x,  ...)
# S4 method for Weibull
Sn(x,  ...)Qn(x, ...)
# S4 method for ANY
Qn(x,  ...)
# S4 method for UnivariateDistribution
Qn(x, q00 = NULL, ...)
# S4 method for AffLinDistribution
Qn(x, ...)
# S4 method for DiscreteDistribution
Qn(x,  ...)
# S4 method for Norm
Qn(x,  ...)
##### Arguments
x

object of class "UnivariateDistribution"

additional arguments to fun or E

q00

numeric or NULL: determines search interval (from -q00 to q00) for Qn; if NULL (default) q00 is set to 10*q(x)(3/4) internally.

low

numeric; lower bound for search interval for median(abs(x-Y)) where Y (a real constant) runs over the range of x; defaults to 0.

upp

numeric; upper bound for search interval for median(abs(x-Y)) where Y (a real constant) runs over the range of x; defaults to 1.01. Is used internally as upp*(mad(x)+abs(median(x)-Y)).

accuracy

numeric; number of grid points for Sn; defaults to 1000.

##### Value

The value of the corresponding functional at the distribution in the argument is computed.

##### Methods

Qn, signature(x = "Any"):

interface to the robustbase-function Qn --- see Qn.

Qn, signature(x = "UnivariateDistribution"):

Qn of univariate distributions.

Qn, signature(x = "DiscreteDistribution"):

Qn of discrete distributions.

Qn, signature(x = "AffLinDistribution"):

abs(x@a) * Qn(x@X0)

Sn, signature(x = "Any"):

interface to the robustbase-function Qn --- see Sn.

Sn, signature(x = "UnivariateDistribution"):

Sn of univariate distributions using pseudo-random variables (Thx to N. Horbenko).

Sn, signature(x = "DiscreteDistribution"):

Sn of discrete distributions.

Sn, signature(x = "AffLinDistribution"):

abs(x@a) * Sn(x@X0)

var, signature(x = "Gumbel"):

exact evaluation using explicit expressions.

var, signature(x = "GPareto"):

exact evaluation using explicit expressions.

var, signature(x = "GEV"):

exact evaluation using explicit expressions.

var, signature(x = "Pareto"):

exact evaluation using explicit expressions.

IQR, signature(x = "Gumbel"):

exact evaluation using explicit expressions.

IQR, signature(x = "GPareto"):

exact evaluation using explicit expressions.

IQR, signature(x = "GEV"):

exact evaluation using explicit expressions.

IQR, signature(x = "Pareto"):

exact evaluation using explicit expressions.

median, signature(x = "Gumbel"):

exact evaluation using explicit expressions.

median, signature(x = "GEV"):

exact evaluation using explicit expressions.

median, signature(x = "GPareto"):

exact evaluation using explicit expressions.

median, signature(x = "Pareto"):

exact evaluation using explicit expressions.

skewness, signature(x = "Gumbel"):

exact evaluation using explicit expressions.

skewness, signature(x = "GEV"):

exact evaluation using explicit expressions.

skewness, signature(x = "GPareto"):

exact evaluation using explicit expressions.

skewness, signature(x = "Pareto"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Gumbel"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "GEV"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "GPareto"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Pareto"):

exact evaluation using explicit expressions.

Sn, signature(x = "Norm"):

exact evaluation using explicit expressions.

Sn, signature(x = "GPareto"):

speeded up using interpolation grid.

Sn, signature(x = "GEV"):

speeded up using interpolation grid.

Sn, signature(x = "Gammad"):

speeded up using interpolation grid.

Sn, signature(x = "Weibull"):

speeded up using interpolation grid.

Sn, signature(x = "Pareto"):

speeded up using interpolation grid.

Qn, signature(x = "Norm"):

exact evaluation using explicit expressions.

##### Caveat

If any of the packages e1071, moments, fBasics is to be used together with distrEx (or RobExtremes) the latter must be attached after any of the first mentioned. Otherwise kurtosis() and skewness() defined as methods in distrEx (or RobExtremes) may get masked. To re-mask, you may use kurtosis <- distrEx::kurtosis; skewness <- distrEx::skewness. See also distrExMASK().

Var, sd, var, IQR, median, mad, sd, Sn, Qn

##### Aliases
• var
• var-methods
• var,Gumbel-method
• var,GPareto-method
• var,GEV-method
• var,Pareto-method
• median
• median-methods
• median,Gumbel-method
• median,GEV-method
• median,GPareto-method
• median,Pareto-method
• IQR
• IQR-methods
• IQR,Gumbel-method
• IQR,GPareto-method
• IQR,GEV-method
• IQR,Pareto-method
• skewness
• skewness-methods
• skewness,Gumbel-method
• skewness,GEV-method
• skewness,GPareto-method
• skewness,Pareto-method
• kurtosis
• kurtosis-methods
• kurtosis,Gumbel-method
• kurtosis,GEV-method
• kurtosis,GPareto-method
• kurtosis,Pareto-method
• Sn
• Sn-methods
• Sn,ANY-method
• Sn,UnivariateDistribution-method
• Sn,Norm-method
• Sn,AffLinDistribution-method
• Sn,GPareto-method
• Sn,Weibull-method
• Sn,GEV-method
• Sn,Pareto-method
• Sn,DiscreteDistribution-method
• Qn
• Qn-methods
• Qn,ANY-method
• Qn,UnivariateDistribution-method
• Qn,Norm-method
• Qn,DiscreteDistribution-method
• Qn,AffLinDistribution-method
##### Examples
# NOT RUN {
# Variance of Exp(1) distribution
G <- GPareto()
var(G)

#median(Exp())
IQR(G)

## note the timing
system.time(print(Sn(GPareto(shape=0.5,scale=2))))
# }
# NOT RUN {
system.time(print(Sn(as(GPareto(shape=0.5,scale=2),"AbscontDistribution"))))
# }

Documentation reproduced from package RobExtremes, version 1.2.0, License: LGPL-3

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