xorbits.numpy.random.poisson(lam=1.0, size=None)[source]#

Draw samples from a Poisson distribution.

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


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

  • 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.


out – Drawn samples from the parameterized Poisson distribution.

Return type

ndarray or scalar

See also


which should be used for new code.


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.



Weisstein, Eric W. “Poisson Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/PoissonDistribution.html


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


Draw samples from the distribution:

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

This docstring was copied from numpy.random.