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 numbersdNULLp"function": cumulative distribution functionq"function": quantile function.withArith.withSim.logExact.lowerExactSymmetry"DistributionSymmetry";
used internally to avoid unnecessary calculations.supportgapsNULL; --- 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 DiscreteDistributionsignature(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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