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
.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
.logExact
.lowerExact
Symmetry
"DistributionSymmetry"
;
used internally to avoid unnecessary calculations.support
gaps
NULL
; --- the gaps slot of
the absolutely continuous part"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")
accessor to
slot p
of acPart(object)
, possibly weighted
by acWeight(object)
;
it has an extra argument CondOrAbs
with default value
"cond"
which if it does not partially match
(by pmatch
) "abs"
, returns exactly
slot p
of acPart(object)
else weighted by
acWeight(object)
.signature(object = "UnivarLebDecDistribution")
accessor to
slot d
of the absolutely continuous part of
the distribution, possibly weighted by acWeight(object)
;
it has an extra argument CondOrAbs
which acts as the one
in p.ac
.signature(object = "UnivarLebDecDistribution")
accessor to
slot q
of acPart(object)
.signature(object = "UnivarLebDecDistribution")
accessor to
slot q
of acPart(object)
.signature(object = "UnivarLebDecDistribution")
accessor to slot p
of discretePart(object)
,
possibly weighted by discreteWeight(object)
;
it has an extra argument CondOrAbs
which acts
as the one in p.ac
.signature(object = "UnivarLebDecDistribution")
accessor to slot d
of discretePart(object)
,
possibly weighted by discreteWeight(object)
;
it has an extra argument CondOrAbs
which acts as
the one in p.ac
.signature(object = "UnivarLebDecDistribution")
accessor to slot q
of discretePart(object)
.signature(object = "UnivarLebDecDistribution")
accessor to slot r
of discretePart(object)
.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 distribution
abs
: 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)
.
sqrt
: signature(x = "UnivarLebDecDistribution")
: exact
image distribution of sqrt(x)
.
sqrt
: signature(x = "AcDcLcDistribution")
: exact image distribution of sqrt(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."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")
"AffLinAbscontDistribution"
,
"AffLinDiscreteDistribution"
, "AffLinUnivarLebDecDistribution"
and called "AffLinDistribution"
which is used for functionals."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.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"))
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