# 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`

##### 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 `Nbinom(prob, size)`

.
This object is a negative binomial distribution.

##### Extends

Class `"DiscreteDistribution"`

, directly.
Class `"UnivariateDistribution"`

, by class `"DiscreteDistribution"`

.
Class `"Distribution"`

, by class `"DiscreteDistribution"`

.

##### See Also

`NbinomParameter-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 1.4, License: GPL (version 2 or later)*