negative_binomial(n, p, size=None)¶
Draw samples from a negative binomial distribution.
Samples are drawn from a negative binomial distribution with specified parameters, n successes and p probability of success where n is > 0 and p is in the interval (0, 1].
- nfloat or array_like of floats
Parameter of the distribution, > 0.
- pfloat or array_like of floats
Parameter of the distribution. Must satisfy 0 < p <= 1.
- sizeint or tuple of ints, optional
Output shape. If the given shape is, e.g.,
(m, n, k), then
m * n * ksamples are drawn. If size is
None(default), a single value is returned if
pare both scalars. Otherwise,
np.broadcast(n, p).sizesamples are drawn.
- outndarray or scalar
Drawn samples from the parameterized negative binomial distribution, where each sample is equal to N, the number of failures that occurred before a total of n successes was reached.
The probability mass function of the negative binomial distribution is
where is the number of successes, is the probability of success, is the number of trials, and is the gamma function. When is an integer, , which is the more common form of this term in the 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.
Weisstein, Eric W. “Negative Binomial Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/NegativeBinomialDistribution.html
Wikipedia, “Negative binomial distribution”, https://en.wikipedia.org/wiki/Negative_binomial_distribution
Draw samples from the distribution:
A real world example. A company drills wild-cat oil exploration wells, each with an estimated probability of success of 0.1. What is the probability of having one success for each successive well, that is what is the probability of a single success after drilling 5 wells, after 6 wells, etc.?
>>> s = np.random.default_rng().negative_binomial(1, 0.1, 100000) >>> for i in range(1, 11): ... probability = sum(s<i) / 100000. ... print(i, "wells drilled, probability of one success =", probability)