Module « numpy.random »

Fonction laplace - module numpy.random

Signature de la fonction laplace

Description

laplace.__doc__

        laplace(loc=0.0, scale=1.0, size=None)

        Draw samples from the Laplace or double exponential distribution with
        specified location (or mean) and scale (decay).

        The Laplace distribution is similar to the Gaussian/normal distribution,
        but is sharper at the peak and has fatter tails. It represents the
        difference between two independent, identically distributed exponential
        random variables.

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

        Parameters
        ----------
        loc : float or array_like of floats, optional
            The position, :math:`\mu`, of the distribution peak. Default is 0.
        scale : float or array_like of floats, optional
            :math:`\lambda`, the exponential decay. Default is 1. Must be non-
            negative.
        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 ``loc`` and ``scale`` are both scalars.
            Otherwise, ``np.broadcast(loc, scale).size`` samples are drawn.

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

        See Also
        --------
        Generator.laplace: which should be used for new code.

        Notes
        -----
        It has the probability density function

        .. math:: f(x; \mu, \lambda) = \frac{1}{2\lambda}
                                       \exp\left(-\frac{|x - \mu|}{\lambda}\right).

        The first law of Laplace, from 1774, states that the frequency
        of an error can be expressed as an exponential function of the
        absolute magnitude of the error, which leads to the Laplace
        distribution. For many problems in economics and health
        sciences, this distribution seems to model the data better
        than the standard Gaussian distribution.

        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] Kotz, Samuel, et. al. "The Laplace Distribution and
               Generalizations, " Birkhauser, 2001.
        .. [3] Weisstein, Eric W. "Laplace Distribution."
               From MathWorld--A Wolfram Web Resource.
               http://mathworld.wolfram.com/LaplaceDistribution.html
        .. [4] Wikipedia, "Laplace distribution",
               https://en.wikipedia.org/wiki/Laplace_distribution

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

        >>> loc, scale = 0., 1.
        >>> s = np.random.laplace(loc, scale, 1000)

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

        >>> import matplotlib.pyplot as plt
        >>> count, bins, ignored = plt.hist(s, 30, density=True)
        >>> x = np.arange(-8., 8., .01)
        >>> pdf = np.exp(-abs(x-loc)/scale)/(2.*scale)
        >>> plt.plot(x, pdf)

        Plot Gaussian for comparison:

        >>> g = (1/(scale * np.sqrt(2 * np.pi)) *
        ...      np.exp(-(x - loc)**2 / (2 * scale**2)))
        >>> plt.plot(x,g)