UnivarLebDecDistribution-class {distr} | R Documentation |
UnivarLebDecDistribution
-class is a class to formalize
a Lebesgue decomposed distribution with a discrete and an
absolutely continuous part; it is a subclass to
class UnivarMixingDistribution
.
Objects can be created by calls of the form
new("UnivarLebDecDistribution", ...)
.
More frequently they are created via the generating function
UnivarLebDecDistribution
.
mixCoeff
:"numeric"
: a vector of length
2 of probabilities for the respective a.c. and discrete part of
the objectmixDistr
:"UnivarDistrList"
: a list of
univariate distributions containing the a.c. and discrete components; must be of
length 2; the first component must be of class "AbscontDistribution"
,
the second of class "DiscreteDistribution"
.img
:"Reals"
: the space of the image of this distribution which has dimension 1
and the name "Real Space" param
:"Parameter"
: the parameter of this distribution, having only the
slot name "Parameter of a discrete distribution" r
:"function"
: generates random numbersd
:NULL
p
:"function"
: cumulative distribution functionq
:"function"
: quantile function.withArith
:.withSim
:
Class "UnivarMixingDistribution"
, directly;
class "UnivariateDistribution"
by class "UnivarMixingDistribution"
class "Distribution"
by class "UnivariateDistribution"
.
signature(object = "UnivarLebDecDistribution")
signature(object = "UnivarLebDecDistribution")
signature(object = "UnivarLebDecDistribution")
signature(object = "UnivarLebDecDistribution")
signature(object = "UnivarLebDecDistribution")
signature(object = "UnivarLebDecDistribution")
signature(object = "UnivarLebDecDistribution")
signature(object = "UnivarLebDecDistribution")
signature(object = "UnivarLebDecDistribution")
signature(object = "UnivarLebDecDistribution")
signature(object = "UnivarLebDecDistribution")
signature(object = "UnivarLebDecDistribution")
signature(object = "UnivarLebDecDistribution")
signature(object = "UnivarLebDecDistribution")
signature(object = "UnivarLebDecDistribution")
signature(object = "UnivarLebDecDistribution")
signature(object = "UnivarLebDecDistribution")
signature(object = "UnivarLebDecDistribution")
signature(object = "UnivarLebDecDistribution")
signature(object = "UnivarLebDecDistribution")
signature(from = "AffLinUnivarLebDecDistribution", to = "UnivarLebDecDistribution")
:
create a "UnivarLebDecDistribution"
object from a "AffLinUnivarLebDecDistribution"
objectsignature(from = "AbscontDistribution", to = "UnivarLebDecDistribution")
:
create a "UnivarLebDecDistribution"
object from a "AbscontDistribution"
objectsignature(from = "DiscreteDistribution", to = "UnivarLebDecDistribution")
:
create a "UnivarLebDecDistribution"
object from a "DiscreteDistribution"
objectsignature(x = "UnivarLebDecDistribution")
: application of a mathematical function, e.g. sin
or
tan
to this discrete distributionabs
{signature(x = "UnivarLebDecDistribution")
: exact image distribution of abs(x)
.}
exp
{signature(x = "UnivarLebDecDistribution")
: exact image distribution of exp(x)
.}
sign
{signature(x = "UnivarLebDecDistribution")
: exact image distribution of sign(x)
.}
sign
{signature(x = "AcDcLcDistribution")
: exact image distribution of sign(x)
.}
sqrt
{signature(x = "AcDcLcDistribution")
: exact image distribution of sqrt(x)
.}
log
{signature(x = "UnivarLebDecDistribution")
: (with optional further argument base
,
defaulting to exp(1)
) exact image distribution of log(x)
.}
log10
{signature(x = "UnivarLebDecDistribution")
: exact image distribution of log10(x)
.}
signature(e1 = "UnivarLebDecDistribution")
: application of `-' to this distributionsignature(e1 = "UnivarLebDecDistribution", e2 = "numeric")
: multiplication of this distribution
by an object of class `numeric'signature(e1 = "UnivarLebDecDistribution", e2 = "numeric")
: division of this distribution
by an object of class `numeric'signature(e1 = "UnivarLebDecDistribution", e2 = "numeric")
: addition of this distribution
to an object of class `numeric'signature(e1 = "UnivarLebDecDistribution", e2 = "numeric")
: subtraction of an object of class `numeric'
from this distribution signature(e1 = "numeric", e2 = "UnivarLebDecDistribution")
: multiplication of this distribution
by an object of class `numeric'signature(e1 = "numeric", e2 = "UnivarLebDecDistribution")
: addition of this distribution
to an object of class `numeric'signature(e1 = "numeric", e2 = "UnivarLebDecDistribution")
: subtraction of this distribution
from an object of class `numeric'signature(e1 = "UnivarLebDecDistribution", e2 = "UnivarLebDecDistribution")
: Convolution of two Lebesgue
decomposed distributions. Result is again of class "UnivarLebDecDistribution"
, but if option
getdistrOption("withSimplify")
is TRUE
it is piped through a call to simplifyD
,
hence may also be of class AbscontDistribution
or DiscreteDistribution
signature(e1 = "UnivarLebDecDistribution", e2 = "UnivarLebDecDistribution")
: Convolution of two Lebesgue
decomposed distributions. The same applies as for the preceding item.
To enhance accuracy of several functionals on distributions,
mainly from package distrEx,
there is an internally used (but exported) subclass
"AffLinUnivarLebDecDistribution"
which has extra slots
a
, b
(both of class "numeric"
), and X0
(of class "UnivarLebDecDistribution"
), to capture the fact
that the object has the same distribution as a * X0 + b
. This is
the class of the return value of methods
signature(e1 = "UnivarLebDecDistribution")
signature(e1 = "UnivarLebDecDistribution", e2 = "numeric")
signature(e1 = "UnivarLebDecDistribution", e2 = "numeric")
signature(e1 = "UnivarLebDecDistribution", e2 = "numeric")
signature(e1 = "UnivarLebDecDistribution", e2 = "numeric")
signature(e1 = "numeric", e2 = "UnivarLebDecDistribution")
signature(e1 = "numeric", e2 = "UnivarLebDecDistribution")
signature(e1 = "numeric", e2 = "UnivarLebDecDistribution")
signature(e1 = "AffLinUnivarLebDecDistribution")
signature(e1 = "AffLinUnivarLebDecDistribution", e2 = "numeric")
signature(e1 = "AffLinUnivarLebDecDistribution", e2 = "numeric")
signature(e1 = "AffLinUnivarLebDecDistribution", e2 = "numeric")
signature(e1 = "AffLinUnivarLebDecDistribution", e2 = "numeric")
signature(e1 = "numeric", e2 = "AffLinUnivarLebDecDistribution")
signature(e1 = "numeric", e2 = "AffLinUnivarLebDecDistribution")
signature(e1 = "numeric", e2 = "AffLinUnivarLebDecDistribution")
There also is a class union of "AffLinAbscontDistribution"
,
"AffLinDiscreteDistribution"
, "AffLinUnivarLebDecDistribution"
and called "AffLinDistribution"
which is used for functionals.
As many operations should be valid no matter whether the operands
are of class "AbscontDistribution"
,
"DiscreteDistribution"
, or "UnivarLebDecDistribution"
,
there is a class union of these classes called "AcDcLcDistribution"
;
in particular methods for "*"
, "/"
,
"^"
(see operators-methods) and methods
Minimum
, Maximum
, Truncate
, and
Huberize
, and convpow
are defined for this
class union.
Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de
Parameter-class
UnivarMixingDistribution-class
DiscreteDistribution-class
AbscontDistribution-class
simplifyD
flat.LCD
wg <- flat.mix(UnivarMixingDistribution(Unif(0,1),Unif(4,5), withSimplify=FALSE)) myLC <- UnivarLebDecDistribution(discretePart=Binom(3,.3), acPart = wg, discreteWeight=.2) myLC p(myLC)(0.3) r(myLC)(30) q(myLC)(0.9) acPart(myLC) plot(myLC) d.discrete(myLC)(2) p.ac(myLC)(0) acWeight(myLC) plot(acPart(myLC)) plot(discretePart(myLC)) gaps(myLC) support(myLC) plot(as(Norm(),"UnivarLebDecDistribution"))