nlcpy.random.Generator.poisson

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

Draws samples from a Poisson distribution.

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

Parameters

lamfloat: 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.

Returns

outndarray: Drawn samples from the parameterized Poisson distribution.

Note

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.

Restriction

If lam is neither a scalar nor None : NotImplementedError occurs.

Examples

Draw samples from the distribution:

>>> import nlcpy as vp
>>> rng = vp.random.default_rng()
>>> s = rng.poisson(5, 10000)

Display histogram of the sample:

>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(s.get(), 14, density=True)
>>> plt.show()

../../_images/nlcpy-random-Generator-poisson-1.png