# numpy.random.RandomState.rayleigh¶

method

random.RandomState.rayleigh(scale=1.0, size=None)

Draw samples from a Rayleigh distribution.

The $$\chi$$ and Weibull distributions are generalizations of the Rayleigh.

Note

New code should use the rayleigh method of a default_rng() instance instead; please see the Quick Start.

Parameters
scalefloat or array_like of floats, optional

Scale, also equals the mode. Must be non-negative. Default is 1.

sizeint 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
outndarray or scalar

Drawn samples from the parameterized Rayleigh distribution.

Generator.rayleigh

which should be used for new code.

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 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

1

Brighton Webs Ltd., “Rayleigh Distribution,” https://web.archive.org/web/20090514091424/http://brighton-webs.co.uk:80/distributions/rayleigh.asp

2

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