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].
Parameters: | n : int
p : float
size : int or tuple of ints
Output shape. If the given shape is, e.g., (m, n, k), then
m * n * k samples are drawn.
|
Returns: | samples : int or ndarray of ints
|
Notes
The probability density for the Negative Binomial distribution is
System Message: WARNING/2 (P(N;n,p) = \binom{N+n-1}{n-1}p^{n}(1-p)^{N},
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where
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is the number of successes,
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is the probability
of success, and
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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.
References
Examples
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