Raleigh and Rican distributions are widely used to model the amplitude fluctuations of received signals from different multipath fading channels.

Rician Distribution is the probability distribution of the magnitude of a circular bivariate normal random variable with potentially non- zero mean. It was named after Stephen O. Rice.

The probability density function of Rician Distribution is

$f(x|\nu ,\sigma)=\dfrac{x}{\sigma^2}exp\left ( \frac{-(x^2+\nu^2)}{2\sigma^2} \right )$

Where Io(z), is the modified Bessel function of the first kind with order zero

Releigh Distribution: It is probability theory and statistics, and it is the continuous probability distribution for positive valued random variables also. It was named after Lord Reyleigh.

It is often observed when overall magnitude of a vector is related to its directional components.

The probability density function od Releigh distribution is:

$f(x;\sigma)=\dfrac{x}{\sigma^2}e^{-x^2/(2\sigma^2)} , x\geq 0$