# randomgen.mtrand.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**float or array_like of floats, optionalScale, also equals the mode. Must be non-negative. Default is 1.

**size**int or tuple of ints, optionalOutput 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 scalarDrawn samples from the parameterized Rayleigh distribution.

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