Module « numpy.random »

Fonction power - module numpy.random

Signature de la fonction power

Description

power.__doc__

        power(a, size=None)

        Draws samples in [0, 1] from a power distribution with positive
        exponent a - 1.

        Also known as the power function distribution.

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

        Parameters
        ----------
        a : float or array_like of floats
            Parameter of the distribution. 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 ``a`` is a scalar.  Otherwise,
            ``np.array(a).size`` samples are drawn.

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

        Raises
        ------
        ValueError
            If a < 1.

        See Also
        --------
        Generator.power: which should be used for new code.

        Notes
        -----
        The probability density function is

        .. math:: P(x; a) = ax^{a-1}, 0 \le x \le 1, a>0.

        The power function distribution is just the inverse of the Pareto
        distribution. It may also be seen as a special case of the Beta
        distribution.

        It is used, for example, in modeling the over-reporting of insurance
        claims.

        References
        ----------
        .. [1] Christian Kleiber, Samuel Kotz, "Statistical size distributions
               in economics and actuarial sciences", Wiley, 2003.
        .. [2] Heckert, N. A. and Filliben, James J. "NIST Handbook 148:
               Dataplot Reference Manual, Volume 2: Let Subcommands and Library
               Functions", National Institute of Standards and Technology
               Handbook Series, June 2003.
               https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/powpdf.pdf

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

        >>> a = 5. # shape
        >>> samples = 1000
        >>> s = np.random.power(a, samples)

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

        >>> import matplotlib.pyplot as plt
        >>> count, bins, ignored = plt.hist(s, bins=30)
        >>> x = np.linspace(0, 1, 100)
        >>> y = a*x**(a-1.)
        >>> normed_y = samples*np.diff(bins)[0]*y
        >>> plt.plot(x, normed_y)
        >>> plt.show()

        Compare the power function distribution to the inverse of the Pareto.

        >>> from scipy import stats # doctest: +SKIP
        >>> rvs = np.random.power(5, 1000000)
        >>> rvsp = np.random.pareto(5, 1000000)
        >>> xx = np.linspace(0,1,100)
        >>> powpdf = stats.powerlaw.pdf(xx,5)  # doctest: +SKIP

        >>> plt.figure()
        >>> plt.hist(rvs, bins=50, density=True)
        >>> plt.plot(xx,powpdf,'r-')  # doctest: +SKIP
        >>> plt.title('np.random.power(5)')

        >>> plt.figure()
        >>> plt.hist(1./(1.+rvsp), bins=50, density=True)
        >>> plt.plot(xx,powpdf,'r-')  # doctest: +SKIP
        >>> plt.title('inverse of 1 + np.random.pareto(5)')

        >>> plt.figure()
        >>> plt.hist(1./(1.+rvsp), bins=50, density=True)
        >>> plt.plot(xx,powpdf,'r-')  # doctest: +SKIP
        >>> plt.title('inverse of stats.pareto(5)')