`scipy.stats._multivariate:multivariate_hypergeom_gen`

source: /scipy/stats/_multivariate.py :5647

Signature

class multivariate_hypergeom_gen ( seed = None )

Members

Summary

A multivariate hypergeometric random variable.

Parameters

%(_doc_default_callparams)s
%(_doc_random_state)s

Methods

pmf(x, m, n): Probability mass function.
logpmf(x, m, n): Log of the probability mass function.
rvs(m, n, size=1, random_state=None): Draw random samples from a multivariate hypergeometric distribution.
mean(m, n): Mean of the multivariate hypergeometric distribution.
var(m, n): Variance of the multivariate hypergeometric distribution.
cov(m, n): Compute the covariance matrix of the multivariate hypergeometric distribution.

Notes

%(_doc_callparams_note)s

The probability mass function for multivariate_hypergeom is

P (X_{1} = x_{1}, X_{2} = x_{2}, \dots, X_{k} = x_{k}) = \frac{( x _{1} m _{1} ) ( x _{2} m _{2} ) \dots ( x _{k} m _{k} )}{( n M )}, (x_{1}, x_{2}, \dots, x_{k}) \in N^{k} with i = 1 \sum k x_{i} = n

where $m_{i}$ are the number of objects of type $i$ , $M$ is the total number of objects in the population (sum of all the $m_{i}$ ), and $n$ is the size of the sample to be taken from the population.

Examples

To evaluate the probability mass function of the multivariate hypergeometric distribution, with a dichotomous population of size :math:`10` and :math:`20`, at a sample of size :math:`12` with :math:`8` objects of the first type and :math:`4` objects of the second type, use:

from scipy.stats import multivariate_hypergeom

✓

multivariate_hypergeom.pmf(x=[8, 4], m=[10, 20], n=12)

✗

The `multivariate_hypergeom` distribution is identical to the corresponding `hypergeom` distribution (tiny numerical differences notwithstanding) when only two types (good and bad) of objects are present in the population as in the example above. Consider another example for a comparison with the hypergeometric distribution:

from scipy.stats import hypergeom

✓

multivariate_hypergeom.pmf(x=[3, 1], m=[10, 5], n=4)
hypergeom.pmf(k=3, M=15, n=4, N=10)

✗

The functions ``pmf``, ``logpmf``, ``mean``, ``var``, ``cov``, and ``rvs`` support broadcasting, under the convention that the vector parameters (``x``, ``m``, and ``n``) are interpreted as if each row along the last axis is a single object. For instance, we can combine the previous two calls to `multivariate_hypergeom` as

multivariate_hypergeom.pmf(x=[[8, 4], [3, 1]], m=[[10, 20], [10, 5]],
                           n=[12, 4])

✗

This broadcasting also works for ``cov``, where the output objects are square matrices of size ``m.shape[-1]``. For example:

multivariate_hypergeom.cov(m=[[7, 9], [10, 15]], n=[8, 12])

✗

That is, ``result[0]`` is equal to ``multivariate_hypergeom.cov(m=[7, 9], n=8)`` and ``result[1]`` is equal to ``multivariate_hypergeom.cov(m=[10, 15], n=12)``. Alternatively, the object may be called (as a function) to fix the `m` and `n` parameters, returning a "frozen" multivariate hypergeometric random variable.

rv = multivariate_hypergeom(m=[10, 20], n=12)

✓

rv.pmf(x=[8, 4])

✗

Aliases

scipy.stats._multivariate.multivariate_hypergeom_gen