numpy.random.RandomState.poisson — NumPy v1.15 Manual (original) (raw)
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 is None (default), a single value is returned if lam is a scalar. Otherwise,np.array(lam).size samples are drawn. |
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| 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 ofk 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 |
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| [2] | Wikipedia, “Poisson distribution”,http://en.wikipedia.org/wiki/Poisson_distribution |
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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))