numpy.random:RandomState.negative_binomial

Notes

The probability mass function of the negative binomial distribution is

where $n$ is the number of successes, $p$ is the probability of success, $N+n$ is the number of trials, and $\Gamma$ is the gamma function. When $n$ is an integer, $\frac{\Gamma (N+n)}{N!\Gamma (n)}=\left(\genfrac{}{}{0ex}{}{N+n-1}{N}\right)$, which is the more common form of this term in the pmf. The negative binomial distribution gives the probability of N failures given n successes, with a success on the last trial.

If one throws a die repeatedly until the third time a "1" appears, then the probability distribution of the number of non-"1"s that appear before the third "1" is a negative binomial distribution.