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Classe « Generator »

Méthode numpy.random.Generator.pareto

Signature de la méthode pareto

def pareto(self, a, size=None) 

Description

help(Generator.pareto)

        pareto(a, size=None)

        Draw samples from a Pareto II (AKA Lomax) distribution with
        specified shape.

        Parameters
        ----------
        a : float or array_like of floats
            Shape of the distribution. Must be positive.
        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 Pareto II distribution.

        See Also
        --------
        scipy.stats.pareto : Pareto I distribution
        scipy.stats.lomax : Lomax (Pareto II) distribution
        scipy.stats.genpareto : Generalized Pareto distribution

        Notes
        -----
        The probability density for the Pareto II distribution is

        .. math:: p(x) = \frac{a}{{x+1}^{a+1}} , x \ge 0

        where :math:`a > 0` is the shape.

        The Pareto II distribution is a shifted and scaled version of the
        Pareto I distribution, which can be found in `scipy.stats.pareto`.

        References
        ----------
        .. [1] Francis Hunt and Paul Johnson, On the Pareto Distribution of
               Sourceforge projects.
        .. [2] Pareto, V. (1896). Course of Political Economy. Lausanne.
        .. [3] Reiss, R.D., Thomas, M.(2001), Statistical Analysis of Extreme
               Values, Birkhauser Verlag, Basel, pp 23-30.
        .. [4] Wikipedia, "Pareto distribution",
               https://en.wikipedia.org/wiki/Pareto_distribution

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

        >>> a = 3.
        >>> rng = np.random.default_rng()
        >>> s = rng.pareto(a, 10000)

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

        >>> import matplotlib.pyplot as plt
        >>> x = np.linspace(0, 3, 50)
        >>> pdf = a / (x+1)**(a+1)
        >>> plt.hist(s, bins=x, density=True, label='histogram')
        >>> plt.plot(x, pdf, linewidth=2, color='r', label='pdf')
        >>> plt.xlim(x.min(), x.max())
        >>> plt.legend()
        >>> plt.show()

        

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