flopscope.numpy.random.RandomState.poisson

fnp.random.RandomState.poisson(self, lam=1.0, size=None)

Draw samples from a Poisson distribution.

Adapted from NumPy docs np.random.RandomState.poisson

Arearandom

Typecounted

Cost

\text{numel}(\text{output})

Flopscope Context

Legacy Poisson sampler; cost = numel(output).

The Poisson distribution is the limit of the binomial distribution for large N.

Note.

New code should use the poisson method of a Generator instance instead; please see the random-quick-start.

Parameters

lam:float or array_like of floats: Expected number of events occurring in a fixed-time interval, must be >= 0. A sequence 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. If size is None (default), a single value is returned if lam is a scalar. Otherwise, flops.array(lam).size samples are drawn.

Returns

out:ndarray or scalar: Drawn samples from the parameterized Poisson distribution.

Notes

The probability mass function (PMF) of Poisson distribution is

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

footnote

1

Weisstein, Eric W. "Poisson Distribution."
From MathWorld--A Wolfram Web Resource.
https://mathworld.wolfram.com/PoissonDistribution.html

footnote

2

Wikipedia, "Poisson distribution",
https://en.wikipedia.org/wiki/Poisson_distribution

Examples

Draw samples from the distribution:

>>> import flopscope.numpy as fnp
>>> s = flops.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 = flops.random.poisson(lam=(100., 500.), size=(100, 2))