mars.tensor.random.rayleigh¶
- mars.tensor.random.rayleigh(scale=1.0, size=None, chunk_size=None, gpu=None, dtype=None)[源代码]¶
Draw samples from a Rayleigh distribution.
The \(\chi\) and Weibull distributions are generalizations of the Rayleigh.
- 参数
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)
, thenm * n * k
samples are drawn. If size isNone
(default), a single value is returned ifscale
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.
- 返回
out – Drawn samples from the parameterized Rayleigh distribution.
- 返回类型
Tensor or scalar
提示
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.
引用
- 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
实际案例
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