numpy.random.RandomState.rayleigh¶

RandomState.
rayleigh
(scale=1.0, size=None)¶ 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)
, thenm * n * k
samples are drawn. If size isNone
(default), a single value is returned ifscale
is a scalar. Otherwise,np.array(scale).size
samples are drawn.
Returns:  out : ndarray or scalar
Drawn samples from the parameterized Rayleigh distribution.
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 zeromean Gaussian distributions. Then the wind speed would have a Rayleigh distribution.
References
[1] Brighton Webs Ltd., “Rayleigh Distribution,” http://www.brightonwebs.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
>>> values = hist(np.random.rayleigh(3, 100000), bins=200, density=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 = np.sqrt(2 / np.pi) * meanvalue >>> s = np.random.rayleigh(modevalue, 1000000)
The percentage of waves larger than 3 meters is:
>>> 100.*sum(s>3)/1000000. 0.087300000000000003