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Méthode numpy.random.Generator.logseries

Signature de la méthode logseries

Description

logseries.__doc__

        logseries(p, size=None)

        Draw samples from a logarithmic series distribution.

        Samples are drawn from a log series distribution with specified
        shape parameter, 0 < ``p`` < 1.

        Parameters
        ----------
        p : float or array_like of floats
            Shape parameter for the distribution.  Must be in the range (0, 1).
        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 ``p`` is a scalar.  Otherwise,
            ``np.array(p).size`` samples are drawn.

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

        See Also
        --------
        scipy.stats.logser : probability density function, distribution or
            cumulative density function, etc.

        Notes
        -----
        The probability mass function for the Log Series distribution is

        .. math:: P(k) = \frac{-p^k}{k \ln(1-p)},

        where p = probability.

        The log series distribution is frequently used to represent species
        richness and occurrence, first proposed by Fisher, Corbet, and
        Williams in 1943 [2].  It may also be used to model the numbers of
        occupants seen in cars [3].

        References
        ----------
        .. [1] Buzas, Martin A.; Culver, Stephen J.,  Understanding regional
               species diversity through the log series distribution of
               occurrences: BIODIVERSITY RESEARCH Diversity & Distributions,
               Volume 5, Number 5, September 1999 , pp. 187-195(9).
        .. [2] Fisher, R.A,, A.S. Corbet, and C.B. Williams. 1943. The
               relation between the number of species and the number of
               individuals in a random sample of an animal population.
               Journal of Animal Ecology, 12:42-58.
        .. [3] D. J. Hand, F. Daly, D. Lunn, E. Ostrowski, A Handbook of Small
               Data Sets, CRC Press, 1994.
        .. [4] Wikipedia, "Logarithmic distribution",
               https://en.wikipedia.org/wiki/Logarithmic_distribution

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

        >>> a = .6
        >>> s = np.random.default_rng().logseries(a, 10000)
        >>> import matplotlib.pyplot as plt
        >>> count, bins, ignored = plt.hist(s)

        #   plot against distribution

        >>> def logseries(k, p):
        ...     return -p**k/(k*np.log(1-p))
        >>> plt.plot(bins, logseries(bins, a) * count.max()/
        ...          logseries(bins, a).max(), 'r')
        >>> plt.show()