var | R Documentation |
Generic functions for the computation of functionals on distributions.
IQR(x, ...)
## S4 method for signature 'UnivariateDistribution'
IQR(x)
## S4 method for signature 'UnivariateCondDistribution'
IQR(x,cond)
## S4 method for signature 'AffLinDistribution'
IQR(x)
## S4 method for signature 'DiscreteDistribution'
IQR(x)
## S4 method for signature 'Arcsine'
IQR(x)
## S4 method for signature 'Cauchy'
IQR(x, propagate.names=getdistrExOption("propagate.names.functionals"))
## S4 method for signature 'Dirac'
IQR(x)
## S4 method for signature 'DExp'
IQR(x)
## S4 method for signature 'Exp'
IQR(x, propagate.names=getdistrExOption("propagate.names.functionals"))
## S4 method for signature 'Geom'
IQR(x, propagate.names=getdistrExOption("propagate.names.functionals"))
## S4 method for signature 'Logis'
IQR(x, propagate.names=getdistrExOption("propagate.names.functionals"))
## S4 method for signature 'Norm'
IQR(x, propagate.names=getdistrExOption("propagate.names.functionals"))
## S4 method for signature 'Unif'
IQR(x, propagate.names=getdistrExOption("propagate.names.functionals"))
median(x, ...)
## S4 method for signature 'UnivariateDistribution'
median(x)
## S4 method for signature 'UnivariateCondDistribution'
median(x,cond)
## S4 method for signature 'AffLinDistribution'
median(x)
## S4 method for signature 'Arcsine'
median(x)
## S4 method for signature 'Cauchy'
median(x, propagate.names=getdistrExOption("propagate.names.functionals"))
## S4 method for signature 'Dirac'
median(x, propagate.names=getdistrExOption("propagate.names.functionals"))
## S4 method for signature 'DExp'
median(x)
## S4 method for signature 'Exp'
median(x, propagate.names=getdistrExOption("propagate.names.functionals"))
## S4 method for signature 'Geom'
median(x, propagate.names=getdistrExOption("propagate.names.functionals"))
## S4 method for signature 'Logis'
median(x, propagate.names=getdistrExOption("propagate.names.functionals"))
## S4 method for signature 'Lnorm'
median(x, propagate.names=getdistrExOption("propagate.names.functionals"))
## S4 method for signature 'Norm'
median(x, propagate.names=getdistrExOption("propagate.names.functionals"))
## S4 method for signature 'Unif'
median(x, propagate.names=getdistrExOption("propagate.names.functionals"))
mad(x, ...)
## S4 method for signature 'UnivariateDistribution'
mad(x)
## S4 method for signature 'AffLinDistribution'
mad(x)
## S4 method for signature 'Cauchy'
mad(x, propagate.names=getdistrExOption("propagate.names.functionals"))
## S4 method for signature 'Dirac'
mad(x)
## S4 method for signature 'DExp'
mad(x)
## S4 method for signature 'Exp'
mad(x, propagate.names=getdistrExOption("propagate.names.functionals"))
## S4 method for signature 'Geom'
mad(x, propagate.names=getdistrExOption("propagate.names.functionals"))
## S4 method for signature 'Logis'
mad(x, propagate.names=getdistrExOption("propagate.names.functionals"))
## S4 method for signature 'Norm'
mad(x, propagate.names=getdistrExOption("propagate.names.functionals"))
## S4 method for signature 'Unif'
mad(x, propagate.names=getdistrExOption("propagate.names.functionals"))
## S4 method for signature 'Arcsine'
mad(x)
sd(x, ...)
## S4 method for signature 'UnivariateDistribution'
sd(x, fun, cond, withCond, useApply,
propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Norm'
sd(x, fun, cond, withCond = FALSE, useApply = TRUE,
propagate.names=getdistrExOption("propagate.names.functionals"), ...)
var(x, ...)
## S4 method for signature 'UnivariateDistribution'
var(x, fun, cond, withCond, useApply, ...)
## S4 method for signature 'AffLinDistribution'
var(x, fun, cond, withCond, useApply, ...)
## S4 method for signature 'CompoundDistribution'
var(x, ...)
## S4 method for signature 'Arcsine'
var(x, ...)
## S4 method for signature 'Binom'
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Beta'
var(x, propagate.names=getdistrExOption("propagate.names.functionals"),...)
## S4 method for signature 'Cauchy'
var(x, ...)
## S4 method for signature 'Chisq'
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Dirac'
var(x, ...)
## S4 method for signature 'DExp'
var(x, ...)
## S4 method for signature 'Exp'
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Fd'
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Gammad'
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Geom'
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Hyper'
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Logis'
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Lnorm'
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Nbinom'
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Norm'
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Pois'
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Td'
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Unif'
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Weibull'
var(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
skewness(x, ...)
## S4 method for signature 'UnivariateDistribution'
skewness(x, fun, cond, withCond, useApply, ...)
## S4 method for signature 'AffLinDistribution'
skewness(x, fun, cond, withCond, useApply, ...)
## S4 method for signature 'Arcsine'
skewness(x, ...)
## S4 method for signature 'Binom'
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Beta'
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Cauchy'
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Chisq'
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Dirac'
skewness(x, ...)
## S4 method for signature 'DExp'
skewness(x, ...)
## S4 method for signature 'Exp'
skewness(x, ...)
## S4 method for signature 'Fd'
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Gammad'
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Geom'
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Hyper'
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Logis'
skewness(x, ...)
## S4 method for signature 'Lnorm'
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Nbinom'
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Norm'
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Pois'
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Td'
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Unif'
skewness(x, ...)
## S4 method for signature 'Weibull'
skewness(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
kurtosis(x, ...)
## S4 method for signature 'UnivariateDistribution'
kurtosis(x, fun, cond, withCond, useApply, ...)
## S4 method for signature 'AffLinDistribution'
kurtosis(x, fun, cond, withCond, useApply, ...)
## S4 method for signature 'Arcsine'
kurtosis(x, ...)
## S4 method for signature 'Binom'
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Beta'
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Cauchy'
kurtosis(x, ...)
## S4 method for signature 'Chisq'
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Dirac'
kurtosis(x, ...)
## S4 method for signature 'DExp'
kurtosis(x, ...)
## S4 method for signature 'Exp'
kurtosis(x, ...)
## S4 method for signature 'Fd'
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Gammad'
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Geom'
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Hyper'
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Logis'
kurtosis(x, ...)
## S4 method for signature 'Lnorm'
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
## S4 method for signature 'Nbinom'
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"),...)
## S4 method for signature 'Norm'
kurtosis(x, ...)
## S4 method for signature 'Pois'
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"),...)
## S4 method for signature 'Td'
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"),...)
## S4 method for signature 'Unif'
kurtosis(x, ...)
## S4 method for signature 'Weibull'
kurtosis(x, propagate.names=getdistrExOption("propagate.names.functionals"), ...)
x |
object of class |
fun |
if missing the (conditional) variance resp. standard deviation is computed
else the (conditional) variance resp. standard deviation of |
cond |
if not missing the conditional variance resp. standard deviation
given |
... |
additional arguments to |
useApply |
logical: should |
withCond |
logical: is |
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
|
The value of the corresponding functional at the distribution in the argument is computed.
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.
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()
.
G. Jay Kerns, gkerns@ysu.edu, has provided a major contribution,
in particular the functionals skewness
and kurtosis
are due to him.
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de
distrExIntegrate
, m1df
, m2df
,
Distribution-class
,
sd
, var
, IQR
,
median
, mad
, sd
,
Sn
, Qn
# 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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