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The Rayleigh distribution

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Distribution name

Rayleigh distribution

Common notation

Parameters

 = scale parameter ()

Domain

Probability density function

Cumulative distribution function

Mean

Variance

Skewness

(Excess) kurtosis

Characteristic function

Here  is the error function, which is defined as:

Other comments

The Rayleigh distribution often arises when the overall magnitude of a vector is related to its directional components

 

Nematrian web functions

 

Functions relating to the above distribution may be accessed via the Nematrian web function library by using a DistributionName of “rayleigh”. Functions relating to a generalised version of this distribution including an additional location (i.e. shift) parameter may be accessed by using a DistributionName of “rayleigh2”, see also including additional shift and scale parameters. For details of other supported probability distributions see here.

 


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