SciPy

numpy.random.poisson

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.

Parameters :

lam : float

Expectation of interval, should be >= 0.

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.

Notes

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.

References

[R222]Weisstein, Eric W. “Poisson Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/PoissonDistribution.html
[R223]Wikipedia, “Poisson distribution”, http://en.wikipedia.org/wiki/Poisson_distribution

Examples

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)
>>> plt.show()

(Source code, png, pdf)

../../_images/numpy-random-poisson-1.png

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