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Fonction hypergeom - module scipy.stats

Signature de la fonction hypergeom

def hypergeom(*args, **kwds) 

Description

hypergeom.__doc__

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.
    
    Methods
    -------
    rvs(M, n, N, loc=0, size=1, random_state=None)
        Random variates.
    pmf(k, M, n, N, loc=0)
        Probability mass function.
    logpmf(k, M, n, N, loc=0)
        Log of the probability mass function.
    cdf(k, M, n, N, loc=0)
        Cumulative distribution function.
    logcdf(k, M, n, N, loc=0)
        Log of the cumulative distribution function.
    sf(k, M, n, N, loc=0)
        Survival function  (also defined as ``1 - cdf``, but `sf` is sometimes more accurate).
    logsf(k, 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, args=(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 fraction alpha [0, 1] of the
        distribution

    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,

    .. math:: p(k, M, n, N) = \frac{\binom{n}{k} \binom{M - n}{N - k}}
                                   {\binom{M}{N}}

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

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

    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()

    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)

    See Also
    --------
    nhypergeom, binom, nbinom