# randomgen.mtrand.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
lamfloat or array_like of floats

Expectation of interval, must be >= 0. A sequence of expectation intervals 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.

Returns
outndarray or scalar

Drawn samples from the parameterized Poisson distribution.

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 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:

>>> 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, density=True)
>>> plt.show()


Draw each 100 values for lambda 100 and 500:

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