numpy.random.RandomState.poisson¶

RandomState.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 :

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.

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

[R161]

Weisstein, Eric W. “Poisson Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/PoissonDistribution.html

[R162]

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-RandomState-poisson-1.png

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