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# Documentation

## Nakagami Distribution

### Definition

The Nakagami distribution has the density function

$2{\left(\frac{\mu }{\omega }\right)}^{\mu }\frac{1}{\Gamma \left(\mu \right)}{x}^{\left(2\mu -1\right)}{e}^{\frac{-\mu }{\omega }{x}^{2}}$

with shape parameter µ and scale parameter ω > 0, for x > 0. If x has a Nakagami distribution with parameters µ and ω, then x2 has a gamma distribution with shape parameter µ and scale parameter ω/µ.

### 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 Fitting app.