Classe « Generator »

Méthode numpy.random.Generator.weibull

Signature de la méthode weibull

Description

weibull.__doc__

        weibull(a, size=None)

        Draw samples from a Weibull distribution.

        Draw samples from a 1-parameter Weibull distribution with the given
        shape parameter `a`.

        .. math:: X = (-ln(U))^{1/a}

        Here, U is drawn from the uniform distribution over (0,1].

        The more common 2-parameter Weibull, including a scale parameter
        :math:`\lambda` is just :math:`X = \lambda(-ln(U))^{1/a}`.

        Parameters
        ----------
        a : float or array_like of floats
            Shape parameter of the distribution.  Must be nonnegative.
        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 Weibull distribution.

        See Also
        --------
        scipy.stats.weibull_max
        scipy.stats.weibull_min
        scipy.stats.genextreme
        gumbel

        Notes
        -----
        The Weibull (or Type III asymptotic extreme value distribution
        for smallest values, SEV Type III, or Rosin-Rammler
        distribution) is one of a class of Generalized Extreme Value
        (GEV) distributions used in modeling extreme value problems.
        This class includes the Gumbel and Frechet distributions.

        The probability density for the Weibull distribution is

        .. math:: p(x) = \frac{a}
                         {\lambda}(\frac{x}{\lambda})^{a-1}e^{-(x/\lambda)^a},

        where :math:`a` is the shape and :math:`\lambda` the scale.

        The function has its peak (the mode) at
        :math:`\lambda(\frac{a-1}{a})^{1/a}`.

        When ``a = 1``, the Weibull distribution reduces to the exponential
        distribution.

        References
        ----------
        .. [1] Waloddi Weibull, Royal Technical University, Stockholm,
               1939 "A Statistical Theory Of The Strength Of Materials",
               Ingeniorsvetenskapsakademiens Handlingar Nr 151, 1939,
               Generalstabens Litografiska Anstalts Forlag, Stockholm.
        .. [2] Waloddi Weibull, "A Statistical Distribution Function of
               Wide Applicability", Journal Of Applied Mechanics ASME Paper
               1951.
        .. [3] Wikipedia, "Weibull distribution",
               https://en.wikipedia.org/wiki/Weibull_distribution

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

        >>> rng = np.random.default_rng()
        >>> a = 5. # shape
        >>> s = rng.weibull(a, 1000)

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

        >>> import matplotlib.pyplot as plt
        >>> x = np.arange(1,100.)/50.
        >>> def weib(x,n,a):
        ...     return (a / n) * (x / n)**(a - 1) * np.exp(-(x / n)**a)

        >>> count, bins, ignored = plt.hist(rng.weibull(5.,1000))
        >>> x = np.arange(1,100.)/50.
        >>> scale = count.max()/weib(x, 1., 5.).max()
        >>> plt.plot(x, weib(x, 1., 5.)*scale)
        >>> plt.show()