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distrEx (version 2.9.5)

var: Generic Functions for the Computation of Functionals

Description

Generic functions for the computation of functionals on distributions.

Usage

IQR(x, ...)
# S4 method for UnivariateDistribution
IQR(x)
# S4 method for UnivariateCondDistribution
IQR(x,cond)
# S4 method for AffLinDistribution
IQR(x)
# S4 method for DiscreteDistribution
IQR(x)
# S4 method for Arcsine
IQR(x)
# S4 method for Cauchy
IQR(x, propagate.names=getdistrExOption("propagate.names.functionals"))
# S4 method for Dirac
IQR(x)
# S4 method for DExp
IQR(x)
# S4 method for Exp
IQR(x, propagate.names=getdistrExOption("propagate.names.functionals"))
# S4 method for Geom
IQR(x, propagate.names=getdistrExOption("propagate.names.functionals"))
# S4 method for Logis
IQR(x, propagate.names=getdistrExOption("propagate.names.functionals"))
# S4 method for Norm
IQR(x, propagate.names=getdistrExOption("propagate.names.functionals"))
# S4 method for Unif
IQR(x, propagate.names=getdistrExOption("propagate.names.functionals"))
median(x, ...)
# S4 method for UnivariateDistribution
median(x)
# S4 method for UnivariateCondDistribution
median(x,cond)
# S4 method for AffLinDistribution
median(x)
# S4 method for Arcsine
median(x)
# S4 method for Cauchy
median(x, propagate.names=getdistrExOption("propagate.names.functionals"))
# S4 method for Dirac
median(x, propagate.names=getdistrExOption("propagate.names.functionals"))
# S4 method for DExp
median(x)
# S4 method for Exp
median(x, propagate.names=getdistrExOption("propagate.names.functionals"))
# S4 method for Geom
median(x, propagate.names=getdistrExOption("propagate.names.functionals"))
# S4 method for Logis
median(x, propagate.names=getdistrExOption("propagate.names.functionals"))
# S4 method for Lnorm
median(x, propagate.names=getdistrExOption("propagate.names.functionals"))
# S4 method for Norm
median(x, propagate.names=getdistrExOption("propagate.names.functionals"))
# S4 method for Unif
median(x, propagate.names=getdistrExOption("propagate.names.functionals"))
mad(x, ...)
# S4 method for UnivariateDistribution
mad(x)
# S4 method for AffLinDistribution
mad(x)
# S4 method for Cauchy
mad(x, propagate.names=getdistrExOption("propagate.names.functionals"))
# S4 method for Dirac
mad(x)
# S4 method for DExp
mad(x)
# S4 method for Exp
mad(x, propagate.names=getdistrExOption("propagate.names.functionals"))
# S4 method for Geom
mad(x, propagate.names=getdistrExOption("propagate.names.functionals"))
# S4 method for Logis
mad(x, propagate.names=getdistrExOption("propagate.names.functionals"))
# S4 method for Norm
mad(x, propagate.names=getdistrExOption("propagate.names.functionals"))
# S4 method for Unif
mad(x, propagate.names=getdistrExOption("propagate.names.functionals"))
# S4 method for Arcsine
mad(x)
sd(x, ...)
# S4 method for UnivariateDistribution
sd(x, fun, cond, withCond, useApply,
          propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Norm
sd(x, fun, cond, withCond = FALSE, useApply = TRUE,
          propagate.names=getdistrExOption("propagate.names.functionals"), ...)
var(x, ...)
# S4 method for UnivariateDistribution
var(x, fun, cond, withCond, useApply, ...)
# S4 method for AffLinDistribution
var(x, fun, cond, withCond, useApply, ...)
# S4 method for CompoundDistribution
var(x, ...)
# S4 method for Arcsine
var(x, ...)
# S4 method for Binom
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Beta
var(x, propagate.names=getdistrExOption("propagate.names.functionals"),...)
# S4 method for Cauchy
var(x, ...)
# S4 method for Chisq
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Dirac
var(x, ...)
# S4 method for DExp
var(x, ...)
# S4 method for Exp
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Fd
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Gammad
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Geom
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Hyper
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Logis
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Lnorm
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Nbinom
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Norm
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Pois
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Td
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Unif
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Weibull
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
skewness(x, ...)
# S4 method for UnivariateDistribution
skewness(x, fun, cond, withCond, useApply, ...)
# S4 method for AffLinDistribution
skewness(x, fun, cond, withCond, useApply, ...)
# S4 method for Arcsine
skewness(x, ...)
# S4 method for Binom
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Beta
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Cauchy
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Chisq
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Dirac
skewness(x, ...)
# S4 method for DExp
skewness(x, ...)
# S4 method for Exp
skewness(x, ...)
# S4 method for Fd
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Gammad
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Geom
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Hyper
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Logis
skewness(x, ...)
# S4 method for Lnorm
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Nbinom
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Norm
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Pois
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Td
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Unif
skewness(x,  ...)
# S4 method for Weibull
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
kurtosis(x, ...)
# S4 method for UnivariateDistribution
kurtosis(x, fun, cond, withCond, useApply, ...)
# S4 method for AffLinDistribution
kurtosis(x, fun, cond, withCond, useApply, ...)
# S4 method for Arcsine
kurtosis(x, ...)
# S4 method for Binom
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Beta
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Cauchy
kurtosis(x, ...)
# S4 method for Chisq
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Dirac
kurtosis(x, ...)
# S4 method for DExp
kurtosis(x, ...)
# S4 method for Exp
kurtosis(x, ...)
# S4 method for Fd
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Gammad
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Geom
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Hyper
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Logis
kurtosis(x, ...)
# S4 method for Lnorm
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
# S4 method for Nbinom
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"),...)
# S4 method for Norm
kurtosis(x, ...)
# S4 method for Pois
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"),...)
# S4 method for Td
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"),...)
# S4 method for Unif
kurtosis(x, ...)
# S4 method for Weibull
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)

Value

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

Arguments

x

object of class "UnivariateDistribution"

fun

if missing the (conditional) variance resp. standard deviation is computed else the (conditional) variance resp. standard deviation of fun is computed.

cond

if not missing the conditional variance resp. standard deviation given cond is computed.

...

additional arguments to fun or E

useApply

logical: should sapply, respectively apply be used to evaluate fund.

withCond

logical: is cond in the argument list of fun.

propagate.names

logical: should names obtained from parameter coordinates be propagated to return values of specific S4 methods for functionals; defaults to the value of the respective distrExoption propagate.names.functionals.

Methods

var, signature(x = "Any"):

interface to the stats-function var --- see var resp. help(var,package="stats").

var, signature(x = "UnivariateDistribution"):

variance of univariate distributions using corresponding E()-method.

var, signature(x = "AffLinDistribution"):

if arguments fun, cond are missing: x@a^2 * var(x@X0) else uses method for signature(x = "UnivariateDistribution")

var, signature(x = "CompoundDistribution"):

if we are in i.i.d. situation (i.e., slot SummandsDistr is of class UnivariateDistribution) the formula \({\rm E}[N]{\rm var}[S]+({\rm E}[S]^2+{\rm var}(S)){\rm var}(N)\) for \(N\) the frequency distribution and \(S\) the summand distribution; else we coerce to "UnivarLebDecDistribution".

sd, signature(x = "Any"):

interface to the stats-function sd --- see sd resp. help(sd,package="stats").

sd, signature(x = "NormParameter"):

returns the slot sd of the parameter of a normal distribution --- see sd resp. help(sd,package="distr").

sd, signature(x = "Norm"):

returns the slot sd of the parameter of a normal distribution --- see sd resp. help(sd,package="distr").

sd, signature(x = "UnivariateDistribution"):

standard deviation of univariate distributions using corresponding E()-method.

IQR, signature(x = "Any"):

interface to the stats-function IQR --- see IQR resp. help(IQR,package="stats").

IQR, signature(x = "UnivariateDistribution"):

interquartile range of univariate distributions using corresponding q()-method.

IQR, signature(x = "UnivariateCondDistribution"):

interquartile range of univariate conditional distributions using corresponding q()-method.

IQR, signature(x = "DiscreteDistribution"):

interquartile range of discrete distributions using corresponding q()-method but taking care that between upper and lower quartile there is 50% probability

IQR, signature(x = "AffLinDistribution"):

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

median, signature(x = "Any"):

interface to the stats-function median --- see median resp. help(var,package="stats").

median, signature(x = "UnivariateDistribution"):

median of univariate distributions using corresponding q()-method.

median, signature(x = "UnivariateCondDistribution"):

median of univariate conditional distributions using corresponding q()-method.

median, signature(x = "AffLinDistribution"):

x@a * median(x@X0) + x@b

mad, signature(x = "Any"):

interface to the stats-function mad --- see mad.

mad, signature(x = "UnivariateDistribution"):

mad of univariate distributions using corresponding q()-method applied to abs(x-median(x)).

mad, signature(x = "AffLinDistribution"):

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

skewness, signature(x = "Any"):

bias free estimation of skewness under normal distribution (default) as well as sample version (by argument sample.version = TRUE).

skewness, signature(x = "UnivariateDistribution"):

skewness of univariate distributions using corresponding E()-method.

skewness, signature(x = "AffLinDistribution"):

if arguments fun, cond are missing: skewness(x@X0) else uses method for signature(x = "UnivariateDistribution")

kurtosis, signature(x = "Any"):

bias free estimation of kurtosis under normal distribution (default) as well as sample version (by argument sample.version = TRUE).

kurtosis, signature(x = "UnivariateDistribution"):

kurtosis of univariate distributions using corresponding E()-method.

kurtosis, signature(x = "AffLinDistribution"):

if arguments fun, cond are missing: kurtosis(x@X0) else uses method for signature(x = "UnivariateDistribution")

var, signature(x = "Arcsine"):

exact evaluation using explicit expressions.

var, signature(x = "Beta"):

for noncentrality 0 exact evaluation using explicit expressions.

var, signature(x = "Binom"):

exact evaluation using explicit expressions.

var, signature(x = "Cauchy"):

exact evaluation using explicit expressions.

var, signature(x = "Chisq"):

exact evaluation using explicit expressions.

var, signature(x = "Dirac"):

exact evaluation using explicit expressions.

var, signature(x = "DExp"):

exact evaluation using explicit expressions.

var, signature(x = "Exp"):

exact evaluation using explicit expressions.

var, signature(x = "Fd"):

exact evaluation using explicit expressions.

var, signature(x = "Gammad"):

exact evaluation using explicit expressions.

var, signature(x = "Geom"):

exact evaluation using explicit expressions.

var, signature(x = "Hyper"):

exact evaluation using explicit expressions.

var, signature(x = "Logis"):

exact evaluation using explicit expressions.

var, signature(x = "Lnorm"):

exact evaluation using explicit expressions.

var, signature(x = "Nbinom"):

exact evaluation using explicit expressions.

var, signature(x = "Norm"):

exact evaluation using explicit expressions.

var, signature(x = "Pois"):

exact evaluation using explicit expressions.

var, signature(x = "Td"):

exact evaluation using explicit expressions.

var, signature(x = "Unif"):

exact evaluation using explicit expressions.

var, signature(x = "Weibull"):

exact evaluation using explicit expressions.

IQR, signature(x = "Arcsine"):

exact evaluation using explicit expressions.

IQR, signature(x = "Cauchy"):

exact evaluation using explicit expressions.

IQR, signature(x = "Dirac"):

exact evaluation using explicit expressions.

IQR, signature(x = "DExp"):

exact evaluation using explicit expressions.

IQR, signature(x = "Exp"):

exact evaluation using explicit expressions.

IQR, signature(x = "Geom"):

exact evaluation using explicit expressions.

IQR, signature(x = "Logis"):

exact evaluation using explicit expressions.

IQR, signature(x = "Norm"):

exact evaluation using explicit expressions.

IQR, signature(x = "Unif"):

exact evaluation using explicit expressions.

median, signature(x = "Arcsine"):

exact evaluation using explicit expressions.

median, signature(x = "Cauchy"):

exact evaluation using explicit expressions.

median, signature(x = "Dirac"):

exact evaluation using explicit expressions.

median, signature(x = "DExp"):

exact evaluation using explicit expressions.

median, signature(x = "Exp"):

exact evaluation using explicit expressions.

median, signature(x = "Geom"):

exact evaluation using explicit expressions.

median, signature(x = "Logis"):

exact evaluation using explicit expressions.

median, signature(x = "Lnorm"):

exact evaluation using explicit expressions.

median, signature(x = "Norm"):

exact evaluation using explicit expressions.

median, signature(x = "Unif"):

exact evaluation using explicit expressions.

mad, signature(x = "Arcsine"):

exact evaluation using explicit expressions.

mad, signature(x = "Cauchy"):

exact evaluation using explicit expressions.

mad, signature(x = "Dirac"):

exact evaluation using explicit expressions.

mad, signature(x = "DExp"):

exact evaluation using explicit expressions.

mad, signature(x = "Exp"):

exact evaluation using explicit expressions.

mad, signature(x = "Geom"):

exact evaluation using explicit expressions.

mad, signature(x = "Logis"):

exact evaluation using explicit expressions.

mad, signature(x = "Norm"):

exact evaluation using explicit expressions.

mad, signature(x = "Unif"):

exact evaluation using explicit expressions.

skewness, signature(x = "Arcsine"):

exact evaluation using explicit expressions.

skewness, signature(x = "Beta"):

for noncentrality 0 exact evaluation using explicit expressions.

skewness, signature(x = "Binom"):

exact evaluation using explicit expressions.

skewness, signature(x = "Cauchy"):

exact evaluation using explicit expressions.

skewness, signature(x = "Chisq"):

exact evaluation using explicit expressions.

skewness, signature(x = "Dirac"):

exact evaluation using explicit expressions.

skewness, signature(x = "DExp"):

exact evaluation using explicit expressions.

skewness, signature(x = "Exp"):

exact evaluation using explicit expressions.

skewness, signature(x = "Fd"):

exact evaluation using explicit expressions.

skewness, signature(x = "Gammad"):

exact evaluation using explicit expressions.

skewness, signature(x = "Geom"):

exact evaluation using explicit expressions.

skewness, signature(x = "Hyper"):

exact evaluation using explicit expressions.

skewness, signature(x = "Logis"):

exact evaluation using explicit expressions.

skewness, signature(x = "Lnorm"):

exact evaluation using explicit expressions.

skewness, signature(x = "Nbinom"):

exact evaluation using explicit expressions.

skewness, signature(x = "Norm"):

exact evaluation using explicit expressions.

skewness, signature(x = "Pois"):

exact evaluation using explicit expressions.

skewness, signature(x = "Td"):

exact evaluation using explicit expressions.

skewness, signature(x = "Unif"):

exact evaluation using explicit expressions.

skewness, signature(x = "Weibull"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Arcsine"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Beta"):

for noncentrality 0 exact evaluation using explicit expressions.

kurtosis, signature(x = "Binom"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Cauchy"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Chisq"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Dirac"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "DExp"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Exp"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Fd"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Gammad"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Geom"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Hyper"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Logis"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Lnorm"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Nbinom"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Norm"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Pois"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Td"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Unif"):

exact evaluation using explicit expressions.

kurtosis, signature(x = "Weibull"):

exact evaluation using explicit expressions.

Author

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

Caveat

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

Acknowledgement

G. Jay Kerns, gkerns@ysu.edu, has provided a major contribution, in particular the functionals skewness and kurtosis are due to him.

See Also

distrExIntegrate, m1df, m2df, Distribution-class,
sd, var, IQR,
median, mad, sd,
Sn, Qn

Examples

Run this code
# Variance of Exp(1) distribution
var(Exp())

#median(Exp())
IQR(Exp())
mad(Exp())

# Variance of N(1,4)^2
var(Norm(mean=1, sd=2), fun = function(x){x^2})
var(Norm(mean=1, sd=2), fun = function(x){x^2}, useApply = FALSE)

## sd -- may equivalently be replaced by var
sd(Pois()) ## uses explicit terms
sd(as(Pois(),"DiscreteDistribution")) ## uses sums
sd(as(Pois(),"UnivariateDistribution")) ## uses simulations
sd(Norm(mean=2), fun = function(x){2*x^2}) ## uses simulations
#
mad(sin(exp(Norm()+2*Pois()))) ## weird

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