#### Previous topic

scipy.stats.geom

#### Next topic

scipy.stats.logser

# scipy.stats.hypergeom

`scipy.stats.``hypergeom` = <scipy.stats._discrete_distns.hypergeom_gen object at 0x450b186c>

  A hypergeometric discrete random variable.

  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.

  As an instance of the `rv_discrete` class, `hypergeom` object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution.

  Notes

  The probability mass function is defined as:

      pmf(k, M, n, N) = choose(n, k) * choose(M - n, N - k) / choose(M, N),
                                     for max(0, N - (M-n)) <= k <= min(n, N)

  The probability mass function above is defined in the “standardized” form. To shift distribution use the `loc` parameter. Specifically, `hypergeom.pmf(k, M, n, N, loc)` is identically equivalent to `hypergeom.pmf(k - loc, M, n, N)`.

  Examples

      >>> from scipy.stats import hypergeom
      >>> import matplotlib.pyplot as plt

  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)

      >>> fig = plt.figure()
      >>> ax = fig.add_subplot(111)
      >>> 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')
      >>> plt.show()

  (Source code)

  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)

  And to generate random numbers:

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

  Methods

  `rvs(M, n, N, loc=0, size=1, random_state=None)` | Random variates.
  `pmf(x, M, n, N, loc=0)` | Probability mass function.
  `logpmf(x, M, n, N, loc=0)` | Log of the probability mass function.
  `cdf(x, M, n, N, loc=0)` | Cumulative density function.
  `logcdf(x, M, n, N, loc=0)` | Log of the cumulative density function.
  `sf(x, M, n, N, loc=0)` | Survival function (`1 - cdf` — sometimes more accurate).
  `logsf(x, M, n, N, loc=0)` | Log of the survival function.
  `ppf(q, M, n, N, loc=0)` | Percent point function (inverse of `cdf` — percentiles).
  `isf(q, M, n, N, loc=0)` | Inverse survival function (inverse of `sf`).
  `stats(M, n, N, loc=0, moments='mv')` | Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
  `entropy(M, n, N, loc=0)` | (Differential) entropy of the RV.
  `expect(func, M, n, N, loc=0, lb=None, ub=None, conditional=False)` | Expected value of a function (of one argument) with respect to the distribution.
  `median(M, n, N, loc=0)` | Median of the distribution.
  `mean(M, n, N, loc=0)` | Mean of the distribution.
  `var(M, n, N, loc=0)` | Variance of the distribution.
  `std(M, n, N, loc=0)` | Standard deviation of the distribution.
  `interval(alpha, M, n, N, loc=0)` | Endpoints of the range that contains alpha percent of the distribution