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Fonction multivariate_normal - module scipy.stats

Signature de la fonction multivariate_normal

def multivariate_normal(mean=None, cov=1, allow_singular=False, seed=None) 

Description

multivariate_normal.__doc__

A multivariate normal random variable.

    The `mean` keyword specifies the mean. The `cov` keyword specifies the
    covariance matrix.

    Methods
    -------
    ``pdf(x, mean=None, cov=1, allow_singular=False)``
        Probability density function.
    ``logpdf(x, mean=None, cov=1, allow_singular=False)``
        Log of the probability density function.
    ``cdf(x, mean=None, cov=1, allow_singular=False, maxpts=1000000*dim, abseps=1e-5, releps=1e-5)``
        Cumulative distribution function.
    ``logcdf(x, mean=None, cov=1, allow_singular=False, maxpts=1000000*dim, abseps=1e-5, releps=1e-5)``
        Log of the cumulative distribution function.
    ``rvs(mean=None, cov=1, size=1, random_state=None)``
        Draw random samples from a multivariate normal distribution.
    ``entropy()``
        Compute the differential entropy of the multivariate normal.

    Parameters
    ----------
    x : array_like
        Quantiles, with the last axis of `x` denoting the components.
    mean : array_like, optional
        Mean of the distribution (default zero)
    cov : array_like, optional
        Covariance matrix of the distribution (default one)
    allow_singular : bool, optional
        Whether to allow a singular covariance matrix.  (Default: False)
    random_state : {None, int, `numpy.random.Generator`,
                    `numpy.random.RandomState`}, optional
    
        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
        singleton is used.
        If `seed` is an int, a new ``RandomState`` instance is used,
        seeded with `seed`.
        If `seed` is already a ``Generator`` or ``RandomState`` instance then
        that instance is used.

    Alternatively, the object may be called (as a function) to fix the mean
    and covariance parameters, returning a "frozen" multivariate normal
    random variable:

    rv = multivariate_normal(mean=None, cov=1, allow_singular=False)
        - Frozen object with the same methods but holding the given
          mean and covariance fixed.

    Notes
    -----
    Setting the parameter `mean` to `None` is equivalent to having `mean`
        be the zero-vector. The parameter `cov` can be a scalar, in which case
        the covariance matrix is the identity times that value, a vector of
        diagonal entries for the covariance matrix, or a two-dimensional
        array_like.
        

    The covariance matrix `cov` must be a (symmetric) positive
    semi-definite matrix. The determinant and inverse of `cov` are computed
    as the pseudo-determinant and pseudo-inverse, respectively, so
    that `cov` does not need to have full rank.

    The probability density function for `multivariate_normal` is

    .. math::

        f(x) = \frac{1}{\sqrt{(2 \pi)^k \det \Sigma}}
               \exp\left( -\frac{1}{2} (x - \mu)^T \Sigma^{-1} (x - \mu) \right),

    where :math:`\mu` is the mean, :math:`\Sigma` the covariance matrix,
    and :math:`k` is the dimension of the space where :math:`x` takes values.

    .. versionadded:: 0.14.0

    Examples
    --------
    >>> import matplotlib.pyplot as plt
    >>> from scipy.stats import multivariate_normal

    >>> x = np.linspace(0, 5, 10, endpoint=False)
    >>> y = multivariate_normal.pdf(x, mean=2.5, cov=0.5); y
    array([ 0.00108914,  0.01033349,  0.05946514,  0.20755375,  0.43939129,
            0.56418958,  0.43939129,  0.20755375,  0.05946514,  0.01033349])
    >>> fig1 = plt.figure()
    >>> ax = fig1.add_subplot(111)
    >>> ax.plot(x, y)

    The input quantiles can be any shape of array, as long as the last
    axis labels the components.  This allows us for instance to
    display the frozen pdf for a non-isotropic random variable in 2D as
    follows:

    >>> x, y = np.mgrid[-1:1:.01, -1:1:.01]
    >>> pos = np.dstack((x, y))
    >>> rv = multivariate_normal([0.5, -0.2], [[2.0, 0.3], [0.3, 0.5]])
    >>> fig2 = plt.figure()
    >>> ax2 = fig2.add_subplot(111)
    >>> ax2.contourf(x, y, rv.pdf(pos))