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# scipy.stats.hypergeom

`scipy.stats.``hypergeom` = <scipy.stats.distributions.hypergeom_gen object at 0x4ad9ad0>

  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.

  Discrete random variables are defined from a standard form and may require some shape parameters to complete its specification. Any optional keyword parameters can be passed to the methods of the RV object as given below:

  Parameters : | x : array_like quantiles q : array_like lower or upper tail probability M, n, N : array_like shape parameters loc : array_like, optional location parameter (default=0) scale : array_like, optional scale parameter (default=1) size : int or tuple of ints, optional shape of random variates (default computed from input arguments ) moments : str, optional composed of letters [‘mvsk’] specifying which moments to compute where ‘m’ = mean, ‘v’ = variance, ‘s’ = (Fisher’s) skew and ‘k’ = (Fisher’s) kurtosis. (default=’mv’) Alternatively, the object may be called (as a function) to fix the shape and : location parameters returning a “frozen” discrete RV object: : rv = hypergeom(M, n, N, loc=0) : Frozen RV object with the same methods but holding the given shape and location fixed.

  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 N - (M-n) <= k <= min(m,N)

  Examples

      >>> from scipy.stats import hypergeom

  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()

  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 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

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