# mars.tensor.random.poisson¶

mars.tensor.random.poisson(lam=1.0, size=None, chunk_size=None, gpu=None, dtype=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) – 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), then m * n * k samples are drawn. If size is None (default), a single value is returned if lam is a scalar. Otherwise, mt.array(lam).size samples are drawn.

• chunk_size (int or tuple of int or tuple of ints, optional) – Desired chunk size on each dimension

• gpu (bool, optional) – Allocate the tensor on GPU if True, False as default

• dtype (data-type, optional) – Data-type of the returned tensor.

Returns

out – Drawn samples from the parameterized Poisson distribution.

Return type

Tensor 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 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 mars.tensor as mt
>>> s = mt.random.poisson(5, 10000)


Display histogram of the sample:

>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(s.execute(), 14, normed=True)
>>> plt.show()


Draw each 100 values for lambda 100 and 500:

>>> s = mt.random.poisson(lam=(100., 500.), size=(100, 2))