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Rician Distribution


The Rician distribution has the density function


with noncentrality parameter s ≥ 0 and scale parameter σ > 0, for x > 0. I0 is the zero-order modified Bessel function of the first kind. If x has a Rician distribution with parameters s and σ, then (x/σ)2 has a noncentral chi-square distribution with two degrees of freedom and noncentrality parameter (s/σ)2.


In communications theory, Nakagami distributions, Rician distributions, and Rayleigh distributions are used to model scattered signals that reach a receiver by multiple paths. Depending on the density of the scatter, the signal will display different fading characteristics. Rayleigh and Nakagami distributions are used to model dense scatters, while Rician distributions model fading with a stronger line-of-sight. Nakagami distributions can be reduced to Rayleigh distributions, but give more control over the extent of the fading.


To estimate distribution parameters, use mle or the Distribution Fitting app.

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