nbinstat (Statistics Toolbox)

Mean and variance of the negative binomial distribution

Syntax

```
[M,V] = nbinstat(R,P)
```

Description

[M,V] = nbinstat(R,P) returns the mean and variance of the negative binomial distribution with parameters R and P. Vector or matrix inputs for R and P must have the same size, which is also the size of M and V. A scalar input for R or P is expanded to a constant matrix with the same dimensions as the other input.

The mean of the negative binomial distribution with parameters r and p is rq/p, where q = 1-p. The variance is rq/p².

The simplest motivation for the negative binomial is the case of successive random trials, each having a constant probability P of success. The number of extra trials you must perform in order to observe a given number R of successes has a negative binomial distribution. However, consistent with a more general interpretation of the negative binomial, nbinstat allows R to be any positive value, including nonintegers.

Example

p = 0.1:0.2:0.9;
r = 1:5;
[R,P] = meshgrid(r,p);
[M,V] = nbinstat(R,P)
M =
    9.0000   18.0000   27.0000   36.0000   45.0000
    2.3333    4.6667    7.0000    9.3333   11.6667
    1.0000    2.0000    3.0000    4.0000    5.0000
    0.4286    0.8571    1.2857    1.7143    2.1429
    0.1111    0.2222    0.3333    0.4444    0.5556
V =
   90.0000  180.0000  270.0000  360.0000  450.0000
    7.7778   15.5556   23.3333   31.1111   38.8889
    2.0000    4.0000    6.0000    8.0000   10.0000
    0.6122    1.2245    1.8367    2.4490    3.0612
    0.1235    0.2469    0.3704    0.4938    0.6173

See Also
nbincdf, nbinfit, nbininv, nbinpdf, nbinrnd

nbinrnd ncfcdf