# DiscreteDistribution-class

##### 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 $1-TruncQuantile$.

##### 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`

##### 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 1.5, License: GPL (version 2 or later)*