Module « numpy.random »

Fonction vonmises - module numpy.random

Signature de la fonction vonmises

Description

vonmises.__doc__

        vonmises(mu, kappa, size=None)

        Draw samples from a von Mises distribution.

        Samples are drawn from a von Mises distribution with specified mode
        (mu) and dispersion (kappa), on the interval [-pi, pi].

        The von Mises distribution (also known as the circular normal
        distribution) is a continuous probability distribution on the unit
        circle.  It may be thought of as the circular analogue of the normal
        distribution.

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

        Parameters
        ----------
        mu : float or array_like of floats
            Mode ("center") of the distribution.
        kappa : float or array_like of floats
            Dispersion of the distribution, has to be >=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 ``mu`` and ``kappa`` are both scalars.
            Otherwise, ``np.broadcast(mu, kappa).size`` samples are drawn.

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

        See Also
        --------
        scipy.stats.vonmises : probability density function, distribution, or
            cumulative density function, etc.
        Generator.vonmises: which should be used for new code.

        Notes
        -----
        The probability density for the von Mises distribution is

        .. math:: p(x) = \frac{e^{\kappa cos(x-\mu)}}{2\pi I_0(\kappa)},

        where :math:`\mu` is the mode and :math:`\kappa` the dispersion,
        and :math:`I_0(\kappa)` is the modified Bessel function of order 0.

        The von Mises is named for Richard Edler von Mises, who was born in
        Austria-Hungary, in what is now the Ukraine.  He fled to the United
        States in 1939 and became a professor at Harvard.  He worked in
        probability theory, aerodynamics, fluid mechanics, and philosophy of
        science.

        References
        ----------
        .. [1] Abramowitz, M. and Stegun, I. A. (Eds.). "Handbook of
               Mathematical Functions with Formulas, Graphs, and Mathematical
               Tables, 9th printing," New York: Dover, 1972.
        .. [2] von Mises, R., "Mathematical Theory of Probability
               and Statistics", New York: Academic Press, 1964.

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

        >>> mu, kappa = 0.0, 4.0 # mean and dispersion
        >>> s = np.random.vonmises(mu, kappa, 1000)

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

        >>> import matplotlib.pyplot as plt
        >>> from scipy.special import i0  # doctest: +SKIP
        >>> plt.hist(s, 50, density=True)
        >>> x = np.linspace(-np.pi, np.pi, num=51)
        >>> y = np.exp(kappa*np.cos(x-mu))/(2*np.pi*i0(kappa))  # doctest: +SKIP
        >>> plt.plot(x, y, linewidth=2, color='r')  # doctest: +SKIP
        >>> plt.show()