method
RandomState.hypergeometric(ngood, nbad, nsample, size=None)
Draw samples from a Hypergeometric distribution.
Samples are drawn from a hypergeometric distribution with specified parameters, ngood
(ways to make a good selection), nbad
(ways to make a bad selection), and nsample
(number of items sampled, which is less than or equal to the sum ngood + nbad
).
Parameters: |
|
---|---|
Returns: |
|
See also
scipy.stats.hypergeom
The probability density for the Hypergeometric distribution is
where and
for P(x) the probability of x
good results in the drawn sample, g = ngood
, b = nbad
, and n = nsample
.
Consider an urn with black and white marbles in it, ngood
of them are black and nbad
are white. If you draw nsample
balls without replacement, then the hypergeometric distribution describes the distribution of black balls in the drawn sample.
Note that this distribution is very similar to the binomial distribution, except that in this case, samples are drawn without replacement, whereas in the Binomial case samples are drawn with replacement (or the sample space is infinite). As the sample space becomes large, this distribution approaches the binomial.
[1] | Lentner, Marvin, “Elementary Applied Statistics”, Bogden and Quigley, 1972. |
[2] | Weisstein, Eric W. “Hypergeometric Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/HypergeometricDistribution.html |
[3] | Wikipedia, “Hypergeometric distribution”, https://en.wikipedia.org/wiki/Hypergeometric_distribution |
Draw samples from the distribution:
>>> ngood, nbad, nsamp = 100, 2, 10 # number of good, number of bad, and number of samples >>> s = np.random.hypergeometric(ngood, nbad, nsamp, 1000) >>> from matplotlib.pyplot import hist >>> hist(s) # note that it is very unlikely to grab both bad items
Suppose you have an urn with 15 white and 15 black marbles. If you pull 15 marbles at random, how likely is it that 12 or more of them are one color?
>>> s = np.random.hypergeometric(15, 15, 15, 100000) >>> sum(s>=12)/100000. + sum(s<=3)/100000. # answer = 0.003 ... pretty unlikely!
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https://docs.scipy.org/doc/numpy-1.17.0/reference/random/generated/numpy.random.mtrand.RandomState.hypergeometric.html