numpy.random.RandomState.poisson¶
-
RandomState.
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: - lam : float or array_like of floats
Expectation of interval, should be >= 0. A sequence of expectation intervals 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)
, 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: - out : ndarray 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 long 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. http://mathworld.wolfram.com/PoissonDistribution.html [2] Wikipedia, “Poisson distribution”, http://en.wikipedia.org/wiki/Poisson_distribution Examples
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))