rayleigh

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rayleigh#

class brainstate.random.rayleigh(scale=1.0, size=None, key=None, dtype=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. Must be non-negative. Default is 1.

  • size (int | Sequence[int] | integer | Sequence[integer] | None) – 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.

  • key (int | Array | ndarray | None) – The key for the random number generator. If not given, the default random number generator is used.

Returns:

out – Drawn samples from the parameterized Rayleigh distribution.

Return type:

ndarray or scalar

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

Examples

Draw values from the distribution and plot the histogram

>>> import brainstate
>>> from matplotlib.pyplot import hist  # noqa
>>> values = hist(brainstate.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 = brainstate.random.rayleigh(modevalue, 1000000)

The percentage of waves larger than 3 meters is:

>>> 100.*sum(s>3)/1000000.
0.087300000000000003 # random
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