## Rician Distribution

### Definition

The Rician distribution has the density function

`${I}_{0}\left(\frac{xs}{{\sigma }^{2}}\right)\frac{x}{{\sigma }^{2}}{e}^{-\left(\frac{{x}^{2}+{s}^{2}}{2{\sigma }^{2}}\right)}$`

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.

### Background

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.

### Parameters

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