Module « numpy.random »

Fonction standard_gamma - module numpy.random

Signature de la fonction standard_gamma

Description

standard_gamma.__doc__

        standard_gamma(shape, size=None)

        Draw samples from a standard Gamma distribution.

        Samples are drawn from a Gamma distribution with specified parameters,
        shape (sometimes designated "k") and scale=1.

        .. note::
            New code should use the ``standard_gamma`` method of a ``default_rng()``
            instance instead; please see the :ref:`random-quick-start`.

        Parameters
        ----------
        shape : float or array_like of floats
            Parameter, must be non-negative.
        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 ``shape`` is a scalar.  Otherwise,
            ``np.array(shape).size`` samples are drawn.

        Returns
        -------
        out : ndarray or scalar
            Drawn samples from the parameterized standard gamma distribution.

        See Also
        --------
        scipy.stats.gamma : probability density function, distribution or
            cumulative density function, etc.
        Generator.standard_gamma: which should be used for new code.

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

        .. math:: p(x) = x^{k-1}\frac{e^{-x/\theta}}{\theta^k\Gamma(k)},

        where :math:`k` is the shape and :math:`\theta` the scale,
        and :math:`\Gamma` is the Gamma function.

        The Gamma distribution is often used to model the times to failure of
        electronic components, and arises naturally in processes for which the
        waiting times between Poisson distributed events are relevant.

        References
        ----------
        .. [1] Weisstein, Eric W. "Gamma Distribution." From MathWorld--A
               Wolfram Web Resource.
               http://mathworld.wolfram.com/GammaDistribution.html
        .. [2] Wikipedia, "Gamma distribution",
               https://en.wikipedia.org/wiki/Gamma_distribution

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

        >>> shape, scale = 2., 1. # mean and width
        >>> s = np.random.standard_gamma(shape, 1000000)

        Display the histogram of the samples, along with
        the probability density function:

        >>> import matplotlib.pyplot as plt
        >>> import scipy.special as sps  # doctest: +SKIP
        >>> count, bins, ignored = plt.hist(s, 50, density=True)
        >>> y = bins**(shape-1) * ((np.exp(-bins/scale))/  # doctest: +SKIP
        ...                       (sps.gamma(shape) * scale**shape))
        >>> plt.plot(bins, y, linewidth=2, color='r')  # doctest: +SKIP
        >>> plt.show()