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Classe « Generator »

Méthode numpy.random.Generator.beta

Signature de la méthode beta

def beta(self, a, b, size=None) 

Description

help(Generator.beta)

        beta(a, b, size=None)

        Draw samples from a Beta distribution.

        The Beta distribution is a special case of the Dirichlet distribution,
        and is related to the Gamma distribution. It has the probability
        distribution function

        .. math:: f(x; a,b) = \frac{1}{B(\alpha, \beta)} x^{\alpha - 1}
                                                         (1 - x)^{\beta - 1},

        where the normalization, B, is the beta function,

        .. math:: B(\alpha, \beta) = \int_0^1 t^{\alpha - 1}
                                     (1 - t)^{\beta - 1} dt.

        It is often seen in Bayesian inference and order statistics.

        Parameters
        ----------
        a : float or array_like of floats
            Alpha, positive (>0).
        b : float or array_like of floats
            Beta, positive (>0).
        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`` and ``b`` are both scalars.
            Otherwise, ``np.broadcast(a, b).size`` samples are drawn.

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

        Examples
        -------- 
        The beta distribution has mean a/(a+b). If ``a == b`` and both 
        are > 1, the distribution is symmetric with mean 0.5.

        >>> rng = np.random.default_rng()
        >>> a, b, size = 2.0, 2.0, 10000
        >>> sample = rng.beta(a=a, b=b, size=size)
        >>> np.mean(sample)
        0.5047328775385895  # may vary
        
        Otherwise the distribution is skewed left or right according to
        whether ``a`` or ``b`` is greater. The distribution is mirror
        symmetric. See for example:
        
        >>> a, b, size = 2, 7, 10000
        >>> sample_left = rng.beta(a=a, b=b, size=size)
        >>> sample_right = rng.beta(a=b, b=a, size=size)
        >>> m_left, m_right = np.mean(sample_left), np.mean(sample_right)
        >>> print(m_left, m_right)
        0.2238596793678923 0.7774613834041182  # may vary
        >>> print(m_left - a/(a+b))
        0.001637457145670096  # may vary
        >>> print(m_right - b/(a+b))
        -0.0003163943736596009  # may vary

        Display the histogram of the two samples:
        
        >>> import matplotlib.pyplot as plt
        >>> plt.hist([sample_left, sample_right], 
        ...          50, density=True, histtype='bar')
        >>> plt.show()
        
        References
        ----------
        .. [1] Wikipedia, "Beta distribution",
               https://en.wikipedia.org/wiki/Beta_distribution

        

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