UnivarLebDecDistribution-class

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Class "UnivarLebDecDistribution"

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.

Keywords
distribution
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

.logExact

logical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function

.lowerExact

logical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function

Symmetry

object of class "DistributionSymmetry"; used internally to avoid unnecessary calculations.

support

numeric vector --- the support slot of the discrete part

gaps

(numeric) matrix or NULL; --- the gaps slot of the absolutely continuous part

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") 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).

d.ac

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.

q.ac

signature(object = "UnivarLebDecDistribution") accessor to slot q of acPart(object).

r.ac

signature(object = "UnivarLebDecDistribution") accessor to slot q of acPart(object).

p.discrete

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.

d.discrete

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.

q.discrete

signature(object = "UnivarLebDecDistribution") accessor to slot q of discretePart(object).

r.discrete

signature(object = "UnivarLebDecDistribution") accessor to slot r of discretePart(object).

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).

• 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 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

-

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.

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.

Aliases
• UnivarLebDecDistribution-class
• AffLinUnivarLebDecDistribution-class
• AcDcLcDistribution-class
• acPart
• discretePart
• acPart<-
• discretePart<-
• acPart-methods
• discretePart-methods
• acPart<--methods
• discretePart<--methods
• acPart,UnivarLebDecDistribution-method
• discretePart,UnivarLebDecDistribution-method
• acPart<-,UnivarLebDecDistribution-method
• discretePart<-,UnivarLebDecDistribution-method
• acWeight
• discreteWeight
• acWeight<-
• discreteWeight<-
• acWeight-methods
• discreteWeight-methods
• acWeight<--methods
• discreteWeight<--methods
• acWeight,UnivarLebDecDistribution-method
• discreteWeight,UnivarLebDecDistribution-method
• acWeight<-,UnivarLebDecDistribution-method
• discreteWeight<-,UnivarLebDecDistribution-method
• p.discrete,UnivarLebDecDistribution-method
• d.discrete,UnivarLebDecDistribution-method
• q.discrete,UnivarLebDecDistribution-method
• r.discrete,UnivarLebDecDistribution-method
• p.ac,UnivarLebDecDistribution-method
• d.ac,UnivarLebDecDistribution-method
• q.ac,UnivarLebDecDistribution-method
• r.ac,UnivarLebDecDistribution-method
• p.discrete-methods
• d.discrete-methods
• q.discrete-methods
• r.discrete-methods
• p.ac-methods
• d.ac-methods
• q.ac-methods
• r.ac-methods
• p.discrete
• d.discrete
• q.discrete
• r.discrete
• p.ac
• d.ac
• q.ac
• r.ac
• coerce,AbscontDistribution,UnivarLebDecDistribution-method
• coerce,DiscreteDistribution,UnivarLebDecDistribution-method
• coerce,AffLinUnivarLebDecDistribution,UnivarLebDecDistribution-method
• abs,UnivarLebDecDistribution-method
• log,UnivarLebDecDistribution-method
• log10,UnivarLebDecDistribution-method
• Math,UnivarLebDecDistribution-method
• ^,AcDcLcDistribution,Dirac-method
• exp,UnivarLebDecDistribution-method
• sign,UnivarLebDecDistribution-method
• sign,AcDcLcDistribution-method
• sqrt,UnivarLebDecDistribution-method
• sqrt,AcDcLcDistribution-method
Examples
# NOT RUN {
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)
## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
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"))
# }
Documentation reproduced from package distr, version 2.8.0, License: LGPL-3

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