`numpy.random._generator:Generator.poisson`

Signature

def poisson ( lam = 1.0 , size = None )

Summary

Draw samples from a Poisson distribution.

Extended Summary

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, np.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; λ) = \frac{λ ^{k} e ^{- λ}}{k !}

For events with an expected separation $λ$ the Poisson distribution $f (k; λ)$ describes the probability of $k$ events occurring within the observed interval $λ$ .

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.

Examples

Draw samples from the distribution:

rng = np.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()

✗

Display the histogram and probability mass function:

import matplotlib.pyplot as plt
from scipy import stats
x = np.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))