method
Generator.
rayleigh
Draw samples from a Rayleigh distribution.
The
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Scale, also equals the mode. Must be non-negative. Default is 1.
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, np.array(scale).size samples are drawn.
(m, n, k)
m * n * k
None
scale
np.array(scale).size
Drawn samples from the parameterized Rayleigh distribution.
Notes
The probability density function for the Rayleigh distribution is
System Message: WARNING/2 (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.
References
Brighton Webs Ltd., “Rayleigh Distribution,” https://web.archive.org/web/20090514091424/http://brighton-webs.co.uk:80/distributions/rayleigh.asp
Wikipedia, “Rayleigh distribution” https://en.wikipedia.org/wiki/Rayleigh_distribution
Examples
Draw values from the distribution and plot the histogram
>>> from matplotlib.pyplot import hist >>> rng = np.random.default_rng() >>> values = hist(rng.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 = rng.rayleigh(modevalue, 1000000)
The percentage of waves larger than 3 meters is:
>>> 100.*sum(s>3)/1000000. 0.087300000000000003 # random
