RayleighDistribution

Model a Rayleigh distribution with scale \(\sigma\).

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Declaration

classdef RayleighDistribution < Distribution

Overview

RayleighDistribution implements the Rayleigh distribution with density \(p(z) = \frac{z}{\sigma^{2}} \exp\!\left(-\frac{z^{2}}{2\sigma^{2}}\right), \quad z \ge 0,\) cumulative distribution \(F(z) = 1 - \exp\!\left(-\frac{z^{2}}{2\sigma^{2}}\right), \quad z \ge 0,\) and variance \(\mathrm{variance} = \frac{4-\pi}{2}\sigma^{2}.\) This family is the radial-distance law obtained from two independent zero-mean Gaussian coordinates with common standard deviation \(\sigma.\)

distribution = RayleighDistribution(sigma=1.0);
samples = distribution.rand([1000 1]);

Topics

• Create distributions
  • RayleighDistribution Create a Rayleigh distribution from its scale parameter.
• Inspect distribution properties
  • sigma Scale parameter \(\sigma\).

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