# LatticeDistribution-class

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##### Class "LatticeDistribution"

The LatticeDistribution-class is the mother-class of the classes Binom, Dirac, Geom, Hyper, Nbinom and Poisson. It formalizes a distribution on a regular affine linear lattice.

Keywords
distribution
##### Note

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

##### Objects from the Class

The usual way to generate objects of class LatticeDistribution is to call the generating function LatticeDistribution. Somewhat more flexible, but also proner to inconsistencies is a call to new("LatticeDistribution"), where you may explicitly specify random number generator, (counting) density, cumulative distribution and quantile functions. For conveniance, in this call to new("LatticeDistribution"), an additional possibility is to only specify the random number generator. The function RtoDPQ.d then approximates the three remaining slots d, p and q by random sampling.

##### Extends

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

##### Internal subclass "AffLinLatticeDistribution"

To enhance accuracy of several functionals on distributions, mainly from package distrEx, there is an internally used (but exported) subclass "AffLinLatticeDistribution" which has extra slots a, b (both of class "numeric"), and X0 (of class "LatticeDistribution"), 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 = "LatticeDistribution")} *{signature(e1 = "LatticeDistribution", e2 = "numeric")} /{signature(e1 = "LatticeDistribution", e2 = "numeric")} +{signature(e1 = "LatticeDistribution", e2 = "numeric")} -{signature(e1 = "LatticeDistribution", e2 = "numeric")} *{signature(e1 = "numeric", e2 = "LatticeDistribution")} +{signature(e1 = "numeric", e2 = "LatticeDistribution")} -{signature(e1 = "numeric", e2 = "LatticeDistribution")} -{signature(e1 = "AffLinLatticeDistribution")} *{signature(e1 = "AffLinLatticeDistribution", e2 = "numeric")} /{signature(e1 = "AffLinLatticeDistribution", e2 = "numeric")} +{signature(e1 = "AffLinLatticeDistribution", e2 = "numeric")} -{signature(e1 = "AffLinLatticeDistribution", e2 = "numeric")} *{signature(e1 = "numeric", e2 = "AffLinLatticeDistribution")} +{signature(e1 = "numeric", e2 = "AffLinLatticeDistribution")} -{signature(e1 = "numeric", e2 = "AffLinLatticeDistribution")}

##### code

"AffLinDiscreteDistribution"

##### concept

• discrete distribution
• lattice distribution
• lattice of a distribution
• S4 distribution class
• generating function

LatticeDistribution Parameter-class Lattice-class UnivariateDistribution-class DiscreteDistribution-class Binom-class Dirac-class Geom-class Hyper-class Nbinom-class Pois-class AbscontDistribution-class Reals-class RtoDPQ.d

##### Aliases
• AffLinLatticeDistribution-class
• LatticeDistribution-class
• lattice
• lattice-method
• lattice,LatticeDistribution-method
• initialize,LatticeDistribution-method
• initialize,AffLinLatticeDistribution-method
• coerce,AffLinLatticeDistribution,AffLinDiscreteDistribution-method
##### Examples
B <- Binom(prob = 0.1,size = 10) # B is a Binomial distribution w/ prob=0.1 and size=10.
P <- Pois(lambda = 1) # P is a Poisson distribution with lambda = 1.
D1 <- B+1 # a new Lattice distributions with exact slots d, p, q
D2 <- D1*3 # a new Lattice distributions with exact slots d, p, q
D3 <- B+P # a new Lattice distributions with approximated slots d, p, q
D4 <- D1+P # a new Lattice distributions with approximated slots d, p, q
support(D4) # the (approximated) support of this distribution is 1, 2, ..., 21
r(D4)(1) # one random number generated from this distribution, e.g. 4
d(D4)(1) # The (approximated) density for x=1 is 0.1282716.
p(D4)(1) # The (approximated) probability that x<=1 is 0.1282716.
q(D4)(.5) # The (approximated) 50 percent quantile is 3.
Documentation reproduced from package distr, version 2.0.2, License: LGPL-3

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