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.

lamfloat 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.

sizeint 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.

outndarray or scalar

Drawn samples from the parameterized Poisson distribution.


The Poisson distribution

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

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.



Weisstein, Eric W. “Poisson Distribution.” From MathWorld–A Wolfram Web Resource.


Wikipedia, “Poisson distribution”,


Draw samples from the distribution:

>>> import numpy as np
>>> rng = np.random.default_rng()
>>> s = rng.poisson(5, 10000)

Display histogram of the sample:

>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(s, 14, density=True)

Draw each 100 values for lambda 100 and 500:

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