# DiscreteDistribution-class

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##### Class "DiscreteDistribution"

The DiscreteDistribution-class is the mother-class of the class LatticeDistribution.

Keywords
distribution
##### Note

Working with a computer, we use a finite interval as support which carries at least mass 1-getdistrOption("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.

##### Extends

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

##### 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 operators-methods) and methods Minimum, Maximum, Truncate, and Huberize, and convpow are defined for this class union.

##### concept

• discrete distribution
• lattice distribution
• support of a distribution
• S4 distribution class

Parameter-class UnivariateDistribution-class LatticeDistribution-class AbscontDistribution-class Reals-class RtoDPQ.d

##### Aliases
• DiscreteDistribution-class
• AffLinDiscreteDistribution-class
• initialize,DiscreteDistribution-method
• initialize,AffLinDiscreteDistribution-method
• sqrt,DiscreteDistribution-method
• coerce,DiscreteDistribution,LatticeDistribution-method
##### Examples
# Dirac-measure 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)-1e-5)
p(D2)(support(D2)+1e-5)
p.l(D2)(support(D2))
p.l(D2)(support(D2)-1e-5)
p.l(D2)(support(D2)+1e-5)
q(D2)(pp)
q(D2)(pp-1e-5)
q(D2)(pp+1e-5)
q.r(D2)(pp)
q.r(D2)(pp-1e-5)
q.r(D2)(pp+1e-5)
Documentation reproduced from package distr, version 2.2.3, License: LGPL-3

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