Description Objects from the Class Slots Extends Methods Internal subclass "AffLinDiscreteDistribution" Internal virtual superclass "AcDcLcDistribution" Note Author(s) See Also Examples
The DiscreteDistribution
class is the motherclass of the class LatticeDistribution
.
Objects can be created by calls to new("DiscreteDistribution", ...)
, but more
easily is the use of the generating function "DiscreteDistribution"
.
This generating function, from version 1.9 on, has been moved to this package from package distrEx.
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
Object of class "function"
: density/probability function
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.
Class "UnivariateDistribution"
, directly.
Class "Distribution"
, by class "UnivariateDistribution"
.
signature(.Object = "DiscreteDistribution")
: initialize method
signature(from = "DiscreteDistribution",
to = "LatticeDistribution")
: coerce method to class "LatticeDistribution"
(checks if support is a lattice)
signature(x = "DiscreteDistribution")
: application of a mathematical function, e.g. sin
or tan
to this discrete distribution
abs
: signature(x = "DiscreteDistribution")
: exact image distribution of abs(x)
.
exp
: signature(x = "DiscreteDistribution")
: exact image distribution of exp(x)
.
sign
: signature(x = "DiscreteDistribution")
: exact image distribution of sign(x)
.
sqrt
: signature(x = "DiscreteDistribution")
: exact image distribution of sqrt(x)
.
log
: signature(x = "DiscreteDistribution")
: (with optional further argument base
, defaulting to exp(1)
) exact image distribution of log(x)
.
log10
: signature(x = "DiscreteDistribution")
: exact image distribution of log10(x)
.
gamma
: signature(x = "DiscreteDistribution")
: exact image distribution of gamma(x)
.
lgamma
: signature(x = "DiscreteDistribution")
: exact image distribution of lgamma(x)
.
digamma
: signature(x = "DiscreteDistribution")
: exact image distribution of digamma(x)
.
signature(e1 = "DiscreteDistribution")
: application of ‘’ to this discrete distribution
signature(e1 = "DiscreteDistribution", e2 = "numeric")
: multiplication of this discrete distribution
by an object of class ‘numeric’
signature(e1 = "DiscreteDistribution", e2 = "numeric")
: division of this discrete distribution
by an object of class ‘numeric’
signature(e1 = "DiscreteDistribution", e2 = "numeric")
: addition of this discrete distribution
to an object of class ‘numeric’
signature(e1 = "DiscreteDistribution", e2 = "numeric")
: subtraction of an object of class ‘numeric’
from this discrete distribution
signature(e1 = "numeric", e2 = "DiscreteDistribution")
: multiplication of this discrete distribution
by an object of class ‘numeric’
signature(e1 = "numeric", e2 = "DiscreteDistribution")
: addition of this discrete distribution
to an object of class ‘numeric’
signature(e1 = "numeric", e2 = "DiscreteDistribution")
: subtraction of this discrete distribution
from an object of class ‘numeric’
signature(e1 = "DiscreteDistribution", e2 = "DiscreteDistribution")
: Convolution of two discrete
distributions. The slots p, d and q are approximated on a common grid.
signature(e1 = "DiscreteDistribution", e2 = "DiscreteDistribution")
: Convolution of two discrete
distributions. The slots p, d and q are approximated on a common grid.
signature(object = "DiscreteDistribution")
: returns the support
signature(object = "DiscreteDistribution")
: returns the
left continuous cumulative distribution function, i.e.;
p.l(t) = P(object < t)
signature(object = "DiscreteDistribution")
: returns the
rightcontinuous quantile function, i.e.;
q.r(s)=sup{tP(object>=t)<=s}
signature(object = "DiscreteDistribution")
: plots density, cumulative distribution and quantile
function
To enhance accuracy of several functionals on distributions,
mainly from package distrEx, from version 1.9 of this package on,
there is an internally used (but exported) subclass
"AffLinDiscreteDistribution"
which has extra slots
a
, b
(both of class "numeric"
), and X0
(of class "DiscreteDistribution"
), 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 = "DiscreteDistribution")
signature(e1 = "DiscreteDistribution", e2 = "numeric")
signature(e1 = "DiscreteDistribution", e2 = "numeric")
signature(e1 = "DiscreteDistribution", e2 = "numeric")
signature(e1 = "DiscreteDistribution", e2 = "numeric")
signature(e1 = "numeric", e2 = "DiscreteDistribution")
signature(e1 = "numeric", e2 = "DiscreteDistribution")
signature(e1 = "numeric", e2 = "DiscreteDistribution")
signature(e1 = "AffLinDiscreteDistribution")
signature(e1 = "AffLinDiscreteDistribution", e2 = "numeric")
signature(e1 = "AffLinDiscreteDistribution", e2 = "numeric")
signature(e1 = "AffLinDiscreteDistribution", e2 = "numeric")
signature(e1 = "AffLinDiscreteDistribution", e2 = "numeric")
signature(e1 = "numeric", e2 = "AffLinDiscreteDistribution")
signature(e1 = "numeric", e2 = "AffLinDiscreteDistribution")
signature(e1 = "numeric", e2 = "AffLinDiscreteDistribution")
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 partiucalar methods for "*"
, "/"
,
"^"
(see operatorsmethods) and methods
Minimum
, Maximum
, Truncate
, and
Huberize
, and convpow
are defined for this
class union.
Working with a computer, we use a finite interval as support which
carries at least mass 1getdistrOption("TruncQuantile")
.
Also, we require that support points have distance at least
getdistrOption("DistrResoltion")
, if this condition fails,
upon a suggestion by Jacob van Etten, [email protected],
we use the global option getdistrOption("DistrCollapse")
to
decide whether we use collapsing or not. If we do so, we collapse support
points if they are too close to each other, taking
the (left most) median among them as new support point which accumulates
all the mass of the collapsed points.
With getdistrOption("DistrCollapse")==FALSE
, we at least collapse
points according to the result of unique()
, and if after this
collapsing, the minimal distance is less than getdistrOption("DistrResoltion")
,
we throw an error. By getdistrOption("DistrCollapse.Unique.Warn")
,
we control, whether we throw a warning upon collapsing or not.
Thomas Stabla [email protected],
Florian Camphausen [email protected],
Peter Ruckdeschel [email protected],
Matthias Kohl [email protected]
Parameterclass
UnivariateDistributionclass
LatticeDistributionclass
AbscontDistributionclass
Realsclass
RtoDPQ.d
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20  # Diracmeasure at 0
D1 < DiscreteDistribution(supp = 0)
support(D1)
# simple discrete distribution
D2 < DiscreteDistribution(supp = c(1:5), prob = c(0.1, 0.2, 0.3, 0.2, 0.2))
plot(D2)
(pp < p(D2)(support(D2)))
p(D2)(support(D2)1e5)
p(D2)(support(D2)+1e5)
p.l(D2)(support(D2))
p.l(D2)(support(D2)1e5)
p.l(D2)(support(D2)+1e5)
q(D2)(pp)
q(D2)(pp1e5)
q(D2)(pp+1e5)
## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
q.r(D2)(pp)
q.r(D2)(pp1e5)
q.r(D2)(pp+1e5)

Loading required package: startupmsg
:startupmsg> Utilities for StartUp Messages (version 0.9.5)
:startupmsg>
:startupmsg> For more information see ?"startupmsg",
:startupmsg> NEWS("startupmsg")
Loading required package: sfsmisc
:distr> Object Oriented Implementation of Distributions (version
:distr> 2.7.0)
:distr>
:distr> Attention: Arithmetics on distribution objects are
:distr> understood as operations on corresponding random variables
:distr> (r.v.s); see distrARITH().
:distr>
:distr> Some functions from package 'stats' are intentionally masked
:distr> see distrMASK().
:distr>
:distr> Note that global options are controlled by distroptions()
:distr> c.f. ?"distroptions".
:distr>
:distr> For more information see ?"distr", NEWS("distr"), as well as
:distr> http://distr.rforge.rproject.org/
:distr> Package "distrDoc" provides a vignette to this package as
:distr> well as to several extension packages; try
:distr> vignette("distr").
Attaching package: 'distr'
The following objects are masked from 'package:stats':
df, qqplot, sd
[1] 0
[1] 0.1 0.3 0.6 0.8 1.0
[1] 0.0 0.1 0.3 0.6 0.8
[1] 0.1 0.3 0.6 0.8 1.0
[1] 0.0 0.1 0.3 0.6 0.8
[1] 0.0 0.1 0.3 0.6 0.8
[1] 0.1 0.3 0.6 0.8 1.0
[1] 1 2 3 4 5
[1] 1 2 3 4 5
[1] 2 3 4 5 NaN
Warning message:
In q(D2)(pp + 1e05) : q method of D2 produced NaN's
[1] 2 3 4 5 5
[1] 1 2 3 4 5
[1] 2 3 4 5 NaN
Warning message:
In q.r(D2)(pp + 1e05) : NaN's produced
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