`scipy.stats._discrete_distns:hypergeom_gen`

source: /scipy/stats/_discrete_distns.py :580

Signature

   class     hypergeom_gen (    a    =  0   ,    b    =  inf   ,    name    =  None   ,    badvalue    =  None   ,    moment_tol    =  1e-08   ,    values    =  None   ,    inc    =  1   ,    longname    =  None   ,    shapes    =  None   ,    seed    =  None     )

Members

Summary

A hypergeometric discrete random variable.

Extended Summary

The hypergeometric distribution models drawing objects from a bin. M is the total number of objects, n is total number of Type I objects. The random variate represents the number of Type I objects in N drawn without replacement from the total population.

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Notes

The symbols used to denote the shape parameters (M, n, and N) are not universally accepted. See the Examples for a clarification of the definitions used here.

The probability mass function is defined as,

p (k, M, n, N) = \frac{( k n ) ( N - k M - n )}{( N M )}

for $k \in [max (0, N - M + n), min (n, N)]$ , where the binomial coefficients are defined as,

(k n) \equiv \frac{n !}{k ! ( n - k )!} .

This distribution uses routines from the Boost Math C++ library for the computation of the pmf, cdf, sf and stats methods. ^[1]

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Examples

import numpy as np
from scipy.stats import hypergeom
import matplotlib.pyplot as plt

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Suppose we have a collection of 20 animals, of which 7 are dogs. Then if we want to know the probability of finding a given number of dogs if we choose at random 12 of the 20 animals, we can initialize a frozen distribution and plot the probability mass function:

[M, n, N] = [20, 7, 12]
rv = hypergeom(M, n, N)
x = np.arange(0, n+1)
pmf_dogs = rv.pmf(x)

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fig = plt.figure()
ax = fig.add_subplot(111)

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ax.plot(x, pmf_dogs, 'bo')
ax.vlines(x, 0, pmf_dogs, lw=2)
ax.set_xlabel('# of dogs in our group of chosen animals')
ax.set_ylabel('hypergeom PMF')

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plt.show()

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Instead of using a frozen distribution we can also use `hypergeom` methods directly. To for example obtain the cumulative distribution function, use:

prb = hypergeom.cdf(x, M, n, N)

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And to generate random numbers:

R = hypergeom.rvs(M, n, N, size=10)

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Aliases

scipy.stats._discrete_distns.hypergeom_gen