flopscope.numpy.random.Generator.poisson

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

Draw samples from a Poisson distribution.

Adapted from NumPy docs np.random.Generator.poisson

Arearandom

Typecounted

Cost

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

Flopscope Context

Poisson distribution; cost = numel(output).

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

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:

>>> rng = flops.random.default_rng()
>>> lam, size = 5, 10000
>>> s = rng.poisson(lam=lam, size=size)

Verify the mean and variance, which should be approximately lam:

>>> s.mean(), s.var()
(4.9917 5.1088311)  # may vary

Display the histogram and probability mass function:

>>> import matplotlib.pyplot as plt
>>> from scipy import stats
>>> x = flops.arange(0, 21)
>>> pmf = stats.poisson.pmf(x, mu=lam)
>>> plt.hist(s, bins=x, density=True, width=0.5)
>>> plt.stem(x, pmf, 'C1-')
>>> plt.show()

Draw each 100 values for lambda 100 and 500:

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