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
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
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")
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"
object
signature(from = "AbscontDistribution", to = "UnivarLebDecDistribution")
:
create a "UnivarLebDecDistribution"
object from a "AbscontDistribution"
object
signature(from = "DiscreteDistribution", to = "UnivarLebDecDistribution")
:
create a "UnivarLebDecDistribution"
object from a "DiscreteDistribution"
object
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.
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 operatorsmethods) and methods
Minimum
, Maximum
, Truncate
, and
Huberize
, and convpow
are defined for this
class union.
Peter Ruckdeschel peter.ruckdeschel@unioldenburg.de
Parameterclass
UnivarMixingDistributionclass
DiscreteDistributionclass
AbscontDistributionclass
simplifyD
flat.LCD
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18  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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