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- Statistics - Discussion
Statistics - Rayleigh Distribution
The Rayleigh distribution is a distribution of continuous probability density function. It is named after the English 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 light radiation.
Engineering - to check the lifetime of an object depending upon its age.
Medical Imaging - to model noise variance in magnetic resonance imaging.
The probability density function Rayleigh distribution is defined as:
Formula
${ f(x; \sigma) = \frac{x}{\sigma^2} e^{\frac{-x^2}{2\sigma^2}}, x \ge 0 }$
Where −
${\sigma}$ = scale parameter of the distribution.
The comulative distribution function Rayleigh distribution is defined as:
Formula
${ F(x; \sigma) = 1 - e^{\frac{-x^2}{2\sigma^2}}, x \in [0 \infty}$
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:
${ Var[x] = \sigma^2 \frac{4-\pi}{2} }$