# DiscreteDistribution-class

From distr v1.8
0th

Percentile

##### Class "DiscreteDistribution"

The DiscreteDistribution-class is the mother-class of the classes Binom, Dirac, Geom, Hyper, Nbinom and Poisson. Further discrete distributions can be defined either by declaration of own random number generator, density and cumulative distribution and quantile functions, or as result of a convolution of two discrete distributions or by application of a mathematical operator to a discrete distribution. An additional way is, to specify only the random number generator. The function RtoDPQ.d then approximates the three remaining slots d, p and q by random sampling.

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

Objects can be created by calls of the form new("DiscreteDistribution", r, d, p, q). The result of this call is a discrete distribution.

##### Extends

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

##### See Also

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

##### Aliases
• DiscreteDistribution-class
• initialize,DiscreteDistribution-method
##### Examples
B = Binom(prob=0.1,size=10) # B is a Binomial distribution with prob=0.1 and size=10.
P = Pois(lambda=1) # P is a Poisson distribution with lambda=1.
D1 = B+1 # a new discrete distributions with exact slots d, p, q
D2 = D1*3 # a new discrete distributions with exact slots d, p, q
D3 = B+P # a new discrete distributions with approximated slots d, p, q
D4 = D1+P # a new discrete 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 1.8, License: GPL (version 2 or later)

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