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Rayleigh Distribution
Statistics - Rayleigh Distribution
The Rayleigh distribution is a distribution of continuous probabipty density function. It is named after the Engpsh Lord Rayleigh. This distribution is widely used for the following:
Communications - to model multiple paths of densely scattered signals while reaching a receiver.
Physical Sciences - to model wind speed, wave heights, sound or pght radiation.
Engineering - to check the pfetime of an object depending upon its age.
Medical Imaging - to model noise variance in magnetic resonance imaging.
The probabipty density function Rayleigh distribution is defined as:
Formula
${ f(x; sigma) = frac{x}{sigma^2} e^{frac{-x^2}{2sigma^2}}, x ge 0 }$
Where −
${sigma}$ = scale parameter of the distribution.
The comulative distribution function Rayleigh distribution is defined as:
Formula
${ F(x; sigma) = 1 - e^{frac{-x^2}{2sigma^2}}, x in [0 infty}$
Where −
${sigma}$ = scale parameter of the distribution.
Variance and Expected Value
The expected value or the mean of a Rayleigh distribution is given by:
${ E[x] = sigma sqrt{frac{pi}{2}} }$
The variance of a Rayleigh distribution is given by:
${ Var[x] = sigma^2 frac{4-pi}{2} }$
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