numpy.random.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.


lam : float or sequence of float

Expectation of interval, should be >= 0. A sequence of expectation intervals 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. Default is None, in which case a single value is returned.


samples : ndarray or scalar

The drawn samples, of shape size, if it was provided.


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 long type, a ValueError is raised when lam is within 10 sigma of the maximum representable value.


[R255]Weisstein, Eric W. “Poisson Distribution.” From MathWorld–A Wolfram Web Resource.
[R256]Wikipedia, “Poisson distribution”,


Draw samples from the distribution:

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

Display histogram of the sample:

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

(Source code, png, pdf)


Draw each 100 values for lambda 100 and 500:

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


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