mars.tensor.random.
rayleigh
Draw samples from a Rayleigh distribution.
The \(\chi\) and Weibull distributions are generalizations of the Rayleigh.
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.
(m, n, k)
m * n * k
None
scale
mt.array(scale).size
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.
out – Drawn samples from the parameterized Rayleigh distribution.
Tensor or scalar
Notes
The probability density function for the Rayleigh distribution is
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
Brighton Webs Ltd., “Rayleigh Distribution,” http://www.brighton-webs.co.uk/distributions/rayleigh.asp
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