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 : scalar
Scale, also equals the mode. Should be >= 0.
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. Default is None, in which case a single value is returned.
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 arises if the wind speed and wind direction are both gaussian variables, then the vector wind velocity forms a Rayleigh distribution. The Rayleigh distribution is used to model the expected output from wind turbines.
References
[R167] Brighton Webs Ltd., Rayleigh Distribution, http://www.brighton-webs.co.uk/distributions/rayleigh.asp [R168] 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, 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 = 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