numpy.random.rayleigh(scale=1.0, size=None)
Draw samples from a Rayleigh distribution.
The 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., |
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Returns: |
out : ndarray or scalar Drawn samples from the parameterized Rayleigh distribution. |
The probability density function for the Rayleigh distribution is
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.
[R519520] | Brighton Webs Ltd., “Rayleigh Distribution,” http://www.brighton-webs.co.uk/distributions/rayleigh.asp |
[R520520] | Wikipedia, “Rayleigh distribution” http://en.wikipedia.org/wiki/Rayleigh_distribution |
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 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
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https://docs.scipy.org/doc/numpy-1.14.2/reference/generated/numpy.random.rayleigh.html