# mars.tensor.random.rayleigh¶

mars.tensor.random.rayleigh(scale=1.0, size=None, chunk_size=None, gpu=None, dtype=None)[source]

Draw samples from a Rayleigh distribution.

The $$\chi$$ and Weibull distributions are generalizations of the Rayleigh.

Parameters
• scale (float or array_like of floats, optional) – Scale, also equals the mode. Should be >= 0. Default is 1.

• 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 scale is a scalar. Otherwise, mt.array(scale).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 Rayleigh distribution.

Return type

Tensor or scalar

Notes

The probability density function for the Rayleigh distribution is

$P(x;scale) = \frac{x}{scale^2}e^{\frac{-x^2}{2 \cdotp scale^2}}$

The Rayleigh distribution would arise, for example, if the East and North components of the wind velocity had identical zero-mean Gaussian distributions. Then the wind speed would have a Rayleigh distribution.

References

1

Brighton Webs Ltd., “Rayleigh Distribution,” http://www.brighton-webs.co.uk/distributions/rayleigh.asp

2

Wikipedia, “Rayleigh distribution” http://en.wikipedia.org/wiki/Rayleigh_distribution

Examples

Draw values from the distribution and plot the histogram

>>> import matplotlib.pyplot as plt
>>> import mars.tensor as mt

>>> values = plt.hist(mt.random.rayleigh(3, 100000).execute(), bins=200, normed=True)


Wave heights tend to follow a Rayleigh distribution. If the mean wave height is 1 meter, what fraction of waves are likely to be larger than 3 meters?

>>> meanvalue = 1
>>> modevalue = mt.sqrt(2 / mt.pi) * meanvalue
>>> s = mt.random.rayleigh(modevalue, 1000000)


The percentage of waves larger than 3 meters is:

>>> (100.*mt.sum(s>3)/1000000.).execute()
0.087300000000000003