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# numpy.random.rayleigh

random.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 `Generator` instance instead; please see the Quick start.

  Parameters:
    scale float or array_like of floats, optional

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

    size int 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:
    out ndarray or scalar

      Drawn samples from the parameterized Rayleigh distribution.

  See also

  `random.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