numpy.random.rayleigh — NumPy v1.16 Manual (original) (raw)

numpy.random. 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, optional Scale, also equals the mode. Should be >= 0. Default is 1. size : int or tuple of ints, optional Output shape. If the given shape is, e.g., (m, n, k), thenm * 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

$P(x;scale) = \frac{x}{scale^2}e^{\frac{-x^2}{2 \cdotp scale^2}}$

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

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