# Nbinom-class

##### Class "Nbinom"

The negative binomial distribution with `size`

$= n$, by default $=1$, and
`prob`

$= p$, by default $=0.5$, has density
$$d(x) = \frac{\Gamma(x+n)}{\Gamma(n) x!} p^n (1-p)^x$$
for $x = 0, 1, 2, \ldots$
This represents the number of failures
which occur in a sequence of Bernoulli trials before a target number
of successes is reached.
C.f. `rnbinom`

- 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 `Nbinom(prob, size)`

.
This object is a negative binomial distribution.

##### Extends

Class `"DiscreteDistribution"`

, directly.
Class `"UnivariateDistribution"`

, by class `"DiscreteDistribution"`

.
Class `"Distribution"`

, by class `"DiscreteDistribution"`

.

##### concept

- discrete distribution
- lattice distribution
- Negative Binomial distribution
- S4 parameter class
- generating function

##### See Also

`NbinomParameter-class`

`Geom-class`

`DiscreteDistribution-class`

`Naturals-class`

`rnbinom`

##### Examples

```
N <- Nbinom(prob = 0.5, size = 1) # N is a binomial distribution with prob=0.5 and size=1.
r(N)(1) # one random number generated from this distribution, e.g. 3
d(N)(1) # Density of this distribution is 0.25 for x=1.
p(N)(0.4) # Probability that x<0.4 is 0.5.
q(N)(.1) # x=0 is the smallest value x such that p(B)(x)>=0.1.
size(N) # size of this distribution is 1.
size(N) <- 2 # size of this distribution is now 2.
```

*Documentation reproduced from package distr, version 2.2.3, License: LGPL-3*