method
RandomState.
rayleigh
Draw samples from a Rayleigh distribution.
The
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Note
New code should use the rayleigh method of a default_rng() instance instead; see random-quick-start.
default_rng()
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.
See also
Generator.rayleigh
which should be used for new code.
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 >>> 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 # random
