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The Rice distribution

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The Rice distribution is characterises the magnitude of a circular bivariate normal random vector with potentially non-zero mean.

 

Distribution name

Rice distribution

Common notation

Parameters

 = parameter

 = parameter

Domain

Probability density function

where  is the modified Bessel function of the first kind of order zero, i.e.

Cumulative distribution function

where  is the Marcum Q-function, i.e. .

Mean

Variance

Other comments

The Rayleigh distribution is a special case of the Rice distribution where .

 

Its non-central moments are:

where  is a Laguerre polynomial.

 

Nematrian web functions

 

This distribution is not currently supported within the Nematrian web function library. For details of supported probability distributions see here.

 


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