numpy.random.rayleigh¶

numpy.random.rayleigh(scale=1.0,size=None)¶

Draw samples from a Rayleigh distribution.

The and Weibull distributions are generalizations of theRayleigh.

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 isNone (default),a single value is returned ifscale 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

The Rayleigh distribution would arise, for example, if the Eastand North components of the wind velocity had identical zero-meanGaussian distributions. Then the wind speed would have a Rayleighdistribution.

References

[R264]

Brighton Webs Ltd., “Rayleigh Distribution,”http://www.brighton-webs.co.uk/distributions/rayleigh.asp

[R265]

Wikipedia, “Rayleigh distribution”http://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,normed=True)

Wave heights tend to follow a Rayleigh distribution. If the mean waveheight is 1 meter, what fraction of waves are likely to be larger than 3meters?

>>>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