SciPy

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

Shape of the output. 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