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# numpy.random.Generator.poisson

method

random.Generator.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

  \[f(k; \lambda)=\frac{\lambda^k e^{-\lambda}}{k!}\]

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

  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))