numpy.random.Generator.poisson#
method
- random.Generator.poisson(lam=1.0, size=None)#
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
Expected number of events occurring in a fixed-time interval, must be >= 0. A sequence 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)
, thenm * n * k
samples are drawn. If size isNone
(default), a single value is returned iflam
is a scalar. Otherwise,np.array(lam).size
samples are drawn.
- Returns:
- outndarray or scalar
Drawn samples from the parameterized Poisson distribution.
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 int64 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. https://mathworld.wolfram.com/PoissonDistribution.html
[2]Wikipedia, “Poisson distribution”, https://en.wikipedia.org/wiki/Poisson_distribution
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() (4.9917 5.1088311) # may vary
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))