DiscreteDistributionclass
Class "DiscreteDistribution"
The DiscreteDistribution
class is the motherclass of the class LatticeDistribution
.
 Keywords
 distribution
Note
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, jacobvanetten@yahoo.com,
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.
Objects from the Class
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.
Slots
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.
Extends
Class "UnivariateDistribution"
, directly.
Class "Distribution"
, by class "UnivariateDistribution"
.
Methods
 initialize
signature(.Object = "DiscreteDistribution")
: initialize method coerce
signature(from = "DiscreteDistribution", to = "LatticeDistribution")
: coerce method to class"LatticeDistribution"
(checks if support is a lattice) Math
signature(x = "DiscreteDistribution")
: application of a mathematical function, e.g.sin
ortan
to this discrete distribution
abs
:signature(x = "DiscreteDistribution")
: exact image distribution ofabs(x)
. 
exp
:signature(x = "DiscreteDistribution")
: exact image distribution ofexp(x)
. 
sign
:signature(x = "DiscreteDistribution")
: exact image distribution ofsign(x)
. 
sqrt
:signature(x = "DiscreteDistribution")
: exact image distribution ofsqrt(x)
. 
log
:signature(x = "DiscreteDistribution")
: (with optional further argumentbase
, defaulting toexp(1)
) exact image distribution oflog(x)
. 
log10
:signature(x = "DiscreteDistribution")
: exact image distribution oflog10(x)
. 
gamma
:signature(x = "DiscreteDistribution")
: exact image distribution ofgamma(x)
. 
lgamma
:signature(x = "DiscreteDistribution")
: exact image distribution oflgamma(x)
. 
digamma
:signature(x = "DiscreteDistribution")
: exact image distribution ofdigamma(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. support
signature(object = "DiscreteDistribution")
: returns the support p.l
signature(object = "DiscreteDistribution")
: returns the left continuous cumulative distribution function, i.e.; $p.l(t) = P(object < t)$ q.r
signature(object = "DiscreteDistribution")
: returns the rightcontinuous quantile function, i.e.; $q.r(s)=sup{tP(object>=t)<=s}$< dd=""> plot
signature(object = "DiscreteDistribution")
: plots density, cumulative distribution and quantile function
Internal subclass "AffLinDiscreteDistribution"
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")
"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 partiucalar methods for "*"
, "/"
,
"^"
(see operatorsmethods) and methods
Minimum
, Maximum
, Truncate
, and
Huberize
, and convpow
are defined for this
class union.
See Also
Parameterclass
UnivariateDistributionclass
LatticeDistributionclass
AbscontDistributionclass
Realsclass
RtoDPQ.d
Examples
# 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)
q.r(D2)(pp)
q.r(D2)(pp1e5)
q.r(D2)(pp+1e5)