mkl_random.MKLRandomState.poisson

MKLRandomState.poisson(lam=1.0, size=None, method='POISNORM')

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, should 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. Default is None, in which case a single value is returned.

method‘POISNORM, ‘PTPE’, optional

Sampling method used by Intel MKL. Can also be specified using tokens mkl_random.POISNORM, mkl_random.PTPE

Returns:

samplesndarray or scalar

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

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

[1]

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

[2]

Wikipedia, “Poisson distribution”, http://en.wikipedia.org/wiki/Poisson_distribution

Examples

Draw samples from the distribution:

>>> import numpy as np
>>> s = mkl_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()

Draw each 100 values for lambda 100 and 500:

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