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, ...) # S4 method for Gammad 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().

See Also

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,Gammad-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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