`numpy.random._generator:Generator.rayleigh`

Signature

def rayleigh ( scale = 1.0 , size = None )

Summary

Draw samples from a Rayleigh distribution.

Extended Summary

The $χ$ and Weibull distributions are generalizations of the Rayleigh.

Parameters

scale : float or array_like of floats, optional: Scale, also equals the mode. Must be non-negative. Default is 1.
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. If size is None (default), a single value is returned if scale 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; sc a l e) = \frac{x}{sc a l e ^{2}} e^{\frac{- x ^{2}}{2 \cdot sc a l e ^{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.

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.