Multivariate hypergeometric distribution

The multivariate hypergeometric distribution is a generalization of the hypergeometric distribution.

mpsci.distributions.multivariate_hypergeometric.cov(colors, nsample)

Covariance matrix of the multivariate hypergeometric distribution.

Let n be the length of colors. The n x n covariance matrix is represented as a list of lists, where the length of the outer list and the lengths of the inner lists are all n.

Examples

First configure the default mpmath precision. Also import pprint for nicer printed output.

>>> from pprint import pprint
>>> from mpmath import mp
>>> mp.dps = 25

Some examples of the cov function.

>>> from mpsci.distributions import multivariate_hypergeometric
>>> c = multivariate_hypergeometric.cov([5, 10, 15], 18)
>>> pprint(c)
[[mpf('1.034482758620689655172413793'),
  mpf('-0.4137931034482758620689655172'),
  mpf('-0.6206896551724137931034482759')],
 [mpf('-0.4137931034482758620689655172'),
  mpf('1.655172413793103448275862069'),
  mpf('-1.241379310344827586206896552')],
 [mpf('-0.6206896551724137931034482759'),
  mpf('-1.241379310344827586206896552'),
  mpf('1.862068965517241379310344828')]]
>>> c = multivariate_hypergeometric.cov([1, 2, 4, 8], 6)
>>> pprint(c)
[[mpf('0.24'),
  mpf('-0.03428571428571428571428571429'),
  mpf('-0.06857142857142857142857142857'),
  mpf('-0.1371428571428571428571428571')],
 [mpf('-0.03428571428571428571428571429'),
  mpf('0.4457142857142857142857142857'),
  mpf('-0.1371428571428571428571428571'),
  mpf('-0.2742857142857142857142857143')],
 [mpf('-0.06857142857142857142857142857'),
  mpf('-0.1371428571428571428571428571'),
  mpf('0.7542857142857142857142857143'),
  mpf('-0.5485714285714285714285714286')],
 [mpf('-0.1371428571428571428571428571'),
  mpf('-0.2742857142857142857142857143'),
  mpf('-0.5485714285714285714285714286'),
  mpf('0.96')]]

mpsci.distributions.multivariate_hypergeometric.entropy(colors, nsample)

Entropy of the multivariate hypergeometric distribution.

The entropy is computed using the natural logarithm.

Examples

First configure the default mpmath precision.

>>> from mpmath import mp
>>> mp.dps = 25

Some examples of the entropy function.

>>> from mpsci.distributions import multivariate_hypergeometric
>>> multivariate_hypergeometric.entropy([5, 10, 15], 18)
mpf('3.046643631879764168841250566')

>>> multivariate_hypergeometric.entropy([1, 2, 4, 8], 6)
mpf('2.877874138861812367967354693')

mpsci.distributions.multivariate_hypergeometric.logpmf(point, colors, nsample)

Log of the PMF of the multivariate hypergeometric distribution.

Example

>>> from mpmath import mp
>>> mp.dps = 25
>>> from mpsci.distributions import multivariate_hypergeometric

>>> multivariate_hypergeometric.logpmf((2, 1, 3), [4, 5, 6], 6)
mpf('-2.121263036533174590973082873')

mpsci.distributions.multivariate_hypergeometric.mean(colors, nsample)

Mean of the multivariate hypergeometric distribution.

Examples

First configure the default mpmath precision.

>>> from mpmath import mp
>>> mp.dps = 25

Some examples of the mean function.

>>> from mpsci.distributions import multivariate_hypergeometric
>>> multivariate_hypergeometric.mean([5, 10, 15], 18)
[mpf('3.0'), mpf('6.0'), mpf('9.0')]

>>> multivariate_hypergeometric.mean([1, 2, 4, 8, 16], 20)
[mpf('0.6451612903225806451612903226'),
 mpf('1.290322580645161290322580645'),
 mpf('2.58064516129032258064516129'),
 mpf('5.161290322580645161290322581'),
 mpf('10.32258064516129032258064516')]

mpsci.distributions.multivariate_hypergeometric.pmf(point, colors, nsample)

Probability mass function of the multivariate hypergeometric distribution.

Example

>>> from mpmath import mp
>>> mp.dps = 25
>>> from mpsci.distributions import multivariate_hypergeometric

>>> multivariate_hypergeometric.logpmf((2, 1, 3), [4, 5, 6], 6)
mpf('0.1198801198801198801198801199')

mpsci.distributions.multivariate_hypergeometric.support(colors, nsample)

Generator of the support of the multivariate hypergeometric distribution.

Examples

>>> list(multivariate_hypergeometric.support([4, 5, 6], 6))
[[0, 0, 6],
 [0, 1, 5],
 [0, 2, 4],
 [0, 3, 3],
 [0, 4, 2],
 [0, 5, 1],
 [1, 0, 5],
 [1, 1, 4],
 [1, 2, 3],
 [1, 3, 2],
 [1, 4, 1],
 [1, 5, 0],
 [2, 0, 4],
 [2, 1, 3],
 [2, 2, 2],
 [2, 3, 1],
 [2, 4, 0],
 [3, 0, 3],
 [3, 1, 2],
 [3, 2, 1],
 [3, 3, 0],
 [4, 0, 2],
 [4, 1, 1],
 [4, 2, 0]]