negative_binomial(self, n, p, size=None, chunks='auto', **kwargs)
This docstring was copied from numpy.random.mtrand.RandomState.negative_binomial.
Some inconsistencies with the Dask version may exist.
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].
New code should use the negative_binomial
method of a default_rng()
instance instead; please see the :None:ref:`random-quick-start`.
The probability mass function of the negative binomial distribution is
$$P(N;n,p) = \frac{\Gamma(N+n)}{N!\Gamma(n)}p^{n}(1-p)^{N},$$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, $\frac{\Gamma(N+n)}{N!\Gamma(n)} = \binom{N+n-1}{N}$ , 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.
Parameter of the distribution, > 0.
Parameter of the distribution, >= 0 and <=1.
Output shape. If the given shape is, e.g., (m, n, k)
, then m * n * k
samples are drawn. If size is None
(default), a single value is returned if n
and p
are both scalars. Otherwise, np.broadcast(n, p).size
samples are drawn.
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.
Draw samples from a negative binomial distribution.
Generator.negative_binomial
which should be used for new code.
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.?
This example is valid syntax, but we were not able to check execution>>> s = np.random.negative_binomial(1, 0.1, 100000) # doctest: +SKIPSee :
... for i in range(1, 11): # doctest: +SKIP
... probability = sum(s<i) / 100000.
... print(i, "wells drilled, probability of one success =", probability)
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