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 trials and p probability of success where n is an integer > 0 and p is in the interval [0, 1].
n : int or array_like of ints
Parameter of the distribution, > 0. Floats are also accepted, but they will be truncated to integers.
p : float or array_like of floats
Parameter of the distribution, >= 0 and <=1.
size : int 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.
out : ndarray or scalar
Drawn samples from the parameterized negative binomial distribution, where each sample is equal to N, the number of trials it took to achieve n - 1 successes, N - (n - 1) failures, and a success on the, (N + n)th trial.
The probability density for the negative binomial distribution is
where is the number of successes, is the probability of success, and is the number of trials. The negative binomial distribution gives the probability of n-1 successes and N failures in N+n-1 trials, and success on the (N+n)th 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.
[R177] Weisstein, Eric W. “Negative Binomial Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/NegativeBinomialDistribution.html [R178] Wikipedia, “Negative binomial distribution”, http://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.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