UnivarLebDecDistribution-class {distr}R Documentation

Class "UnivarLebDecDistribution"

Description

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 from the Class

Objects can be created by calls of the form new("UnivarLebDecDistribution", ...). More frequently they are created via the generating function UnivarLebDecDistribution.

Slots

mixCoeff:
Object of class "numeric": a vector of length 2 of probabilities for the respective a.c. and discrete part of the object
mixDistr:
Object of class "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:
Object of class "Reals": the space of the image of this distribution which has dimension 1 and the name "Real Space"
param:
Object of class "Parameter": the parameter of this distribution, having only the slot name "Parameter of a discrete distribution"
r:
Object of class "function": generates random numbers
d:
fixed to NULL
p:
Object of class "function": cumulative distribution function
q:
Object of class "function": quantile function
.withArith:
logical: used internally to issue warnings as to interpretation of arithmetics
.withSim:
logical: used internally to issue warnings as to accuracy

Extends

Class "UnivarMixingDistribution", directly; class "UnivariateDistribution" by class "UnivarMixingDistribution" class "Distribution" by class "UnivariateDistribution".

Methods

show
signature(object = "UnivarLebDecDistribution")
plot
signature(object = "UnivarLebDecDistribution")
acPart
signature(object = "UnivarLebDecDistribution")
acPart<-
signature(object = "UnivarLebDecDistribution")
discretePart
signature(object = "UnivarLebDecDistribution")
discretePart<-
signature(object = "UnivarLebDecDistribution")
acWeight
signature(object = "UnivarLebDecDistribution")
acWeight<-
signature(object = "UnivarLebDecDistribution")
discreteWeight
signature(object = "UnivarLebDecDistribution")
discreteWeight<-
signature(object = "UnivarLebDecDistribution")
p.ac
signature(object = "UnivarLebDecDistribution")
q.ac
signature(object = "UnivarLebDecDistribution")
d.ac
signature(object = "UnivarLebDecDistribution")
r.ac
signature(object = "UnivarLebDecDistribution")
p.discrete
signature(object = "UnivarLebDecDistribution")
q.discrete
signature(object = "UnivarLebDecDistribution")
d.discrete
signature(object = "UnivarLebDecDistribution")
r.discrete
signature(object = "UnivarLebDecDistribution")
support
signature(object = "UnivarLebDecDistribution")
gaps
signature(object = "UnivarLebDecDistribution")
coerce
signature(from = "AffLinUnivarLebDecDistribution", to = "UnivarLebDecDistribution"): create a "UnivarLebDecDistribution" object from a "AffLinUnivarLebDecDistribution" object
coerce
signature(from = "AbscontDistribution", to = "UnivarLebDecDistribution"): create a "UnivarLebDecDistribution" object from a "AbscontDistribution" object
coerce
signature(from = "DiscreteDistribution", to = "UnivarLebDecDistribution"): create a "UnivarLebDecDistribution" object from a "DiscreteDistribution" object
Math
signature(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).}
-
signature(e1 = "UnivarLebDecDistribution"): application of `-' to this distribution
*
signature(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.

Internal subclass "AffLinUnivarLebDecDistribution"

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

There also is a class union of "AffLinAbscontDistribution", "AffLinDiscreteDistribution", "AffLinUnivarLebDecDistribution" and called "AffLinDistribution" which is used for functionals.

Internal virtual superclass "AcDcLcDistribution"

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.

Author(s)

Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de

See Also

Parameter-class UnivarMixingDistribution-class DiscreteDistribution-class AbscontDistribution-class simplifyD flat.LCD

Examples

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"))

[Package distr version 2.0.6 Index]