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Classe « Generator »

Méthode numpy.random.Generator.poisson

Signature de la méthode poisson

def poisson(self, lam=1.0, size=None) 

Description

help(Generator.poisson)

        poisson(lam=1.0, size=None)

        Draw samples from a Poisson distribution.

        The Poisson distribution is the limit of the binomial distribution
        for large N.

        Parameters
        ----------
        lam : float or array_like of floats
            Expected number of events occurring in a fixed-time interval,
            must be >= 0. A sequence must be broadcastable over the requested
            size.
        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 ``lam`` is a scalar. Otherwise,
            ``np.array(lam).size`` samples are drawn.

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

        Notes
        -----
        The probability mass function (PMF) of Poisson distribution is

        .. math:: f(k; \lambda)=\frac{\lambda^k e^{-\lambda}}{k!}

        For events with an expected separation :math:`\lambda` the Poisson
        distribution :math:`f(k; \lambda)` describes the probability of
        :math:`k` events occurring within the observed
        interval :math:`\lambda`.

        Because the output is limited to the range of the C int64 type, a
        ValueError is raised when `lam` is within 10 sigma of the maximum
        representable value.

        References
        ----------
        .. [1] Weisstein, Eric W. "Poisson Distribution."
               From MathWorld--A Wolfram Web Resource.
               https://mathworld.wolfram.com/PoissonDistribution.html
        .. [2] Wikipedia, "Poisson distribution",
               https://en.wikipedia.org/wiki/Poisson_distribution

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

        >>> rng = np.random.default_rng()
        >>> lam, size = 5, 10000
        >>> s = rng.poisson(lam=lam, size=size)

        Verify the mean and variance, which should be approximately ``lam``:
        
        >>> s.mean(), s.var()
        (4.9917 5.1088311)  # may vary

        Display the histogram and probability mass function:

        >>> import matplotlib.pyplot as plt
        >>> from scipy import stats
        >>> x = np.arange(0, 21)
        >>> pmf = stats.poisson.pmf(x, mu=lam)
        >>> plt.hist(s, bins=x, density=True, width=0.5)
        >>> plt.stem(x, pmf, 'C1-')
        >>> plt.show()

        Draw each 100 values for lambda 100 and 500:

        >>> s = rng.poisson(lam=(100., 500.), size=(100, 2))

        

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