brainpy.math.random.poisson#
- brainpy.math.random.poisson(lam=1.0, size=None, key=None)[source]#
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) – 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)
, 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 – Drawn samples from the parameterized Poisson distribution.
- Return type:
ndarray or scalar
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
Examples
Draw samples from the distribution:
>>> import numpy as np >>> s = bm.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 = bm.random.poisson(lam=(100., 500.), size=(100, 2))