Classe « Generator »

Méthode numpy.random.Generator.hypergeometric

Signature de la méthode hypergeometric

Description

hypergeometric.__doc__

        hypergeometric(ngood, nbad, nsample, size=None)

        Draw samples from a Hypergeometric distribution.

        Samples are drawn from a hypergeometric distribution with specified
        parameters, `ngood` (ways to make a good selection), `nbad` (ways to make
        a bad selection), and `nsample` (number of items sampled, which is less
        than or equal to the sum ``ngood + nbad``).

        Parameters
        ----------
        ngood : int or array_like of ints
            Number of ways to make a good selection.  Must be nonnegative and
            less than 10**9.
        nbad : int or array_like of ints
            Number of ways to make a bad selection.  Must be nonnegative and
            less than 10**9.
        nsample : int or array_like of ints
            Number of items sampled.  Must be nonnegative and less than
            ``ngood + nbad``.
        size : int or tuple of ints, optional
            Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
            ``m * n * k`` samples are drawn.  If size is ``None`` (default),
            a single value is returned if `ngood`, `nbad`, and `nsample`
            are all scalars.  Otherwise, ``np.broadcast(ngood, nbad, nsample).size``
            samples are drawn.

        Returns
        -------
        out : ndarray or scalar
            Drawn samples from the parameterized hypergeometric distribution. Each
            sample is the number of good items within a randomly selected subset of
            size `nsample` taken from a set of `ngood` good items and `nbad` bad items.

        See Also
        --------
        multivariate_hypergeometric : Draw samples from the multivariate
            hypergeometric distribution.
        scipy.stats.hypergeom : probability density function, distribution or
            cumulative density function, etc.

        Notes
        -----
        The probability density for the Hypergeometric distribution is

        .. math:: P(x) = \frac{\binom{g}{x}\binom{b}{n-x}}{\binom{g+b}{n}},

        where :math:`0 \le x \le n` and :math:`n-b \le x \le g`

        for P(x) the probability of ``x`` good results in the drawn sample,
        g = `ngood`, b = `nbad`, and n = `nsample`.

        Consider an urn with black and white marbles in it, `ngood` of them
        are black and `nbad` are white. If you draw `nsample` balls without
        replacement, then the hypergeometric distribution describes the
        distribution of black balls in the drawn sample.

        Note that this distribution is very similar to the binomial
        distribution, except that in this case, samples are drawn without
        replacement, whereas in the Binomial case samples are drawn with
        replacement (or the sample space is infinite). As the sample space
        becomes large, this distribution approaches the binomial.

        The arguments `ngood` and `nbad` each must be less than `10**9`. For
        extremely large arguments, the algorithm that is used to compute the
        samples [4]_ breaks down because of loss of precision in floating point
        calculations.  For such large values, if `nsample` is not also large,
        the distribution can be approximated with the binomial distribution,
        `binomial(n=nsample, p=ngood/(ngood + nbad))`.

        References
        ----------
        .. [1] Lentner, Marvin, "Elementary Applied Statistics", Bogden
               and Quigley, 1972.
        .. [2] Weisstein, Eric W. "Hypergeometric Distribution." From
               MathWorld--A Wolfram Web Resource.
               http://mathworld.wolfram.com/HypergeometricDistribution.html
        .. [3] Wikipedia, "Hypergeometric distribution",
               https://en.wikipedia.org/wiki/Hypergeometric_distribution
        .. [4] Stadlober, Ernst, "The ratio of uniforms approach for generating
               discrete random variates", Journal of Computational and Applied
               Mathematics, 31, pp. 181-189 (1990).

        Examples
        --------
        Draw samples from the distribution:

        >>> rng = np.random.default_rng()
        >>> ngood, nbad, nsamp = 100, 2, 10
        # number of good, number of bad, and number of samples
        >>> s = rng.hypergeometric(ngood, nbad, nsamp, 1000)
        >>> from matplotlib.pyplot import hist
        >>> hist(s)
        #   note that it is very unlikely to grab both bad items

        Suppose you have an urn with 15 white and 15 black marbles.
        If you pull 15 marbles at random, how likely is it that
        12 or more of them are one color?

        >>> s = rng.hypergeometric(15, 15, 15, 100000)
        >>> sum(s>=12)/100000. + sum(s<=3)/100000.
        #   answer = 0.003 ... pretty unlikely!