Rice Distribution

$$P(Z) = {Z\over\sigma^2} \mathop{\rm exp}\nolimits \left({-{Z... ...\sigma^2}}\right)I_0\left({Z\vert V\vert\over\sigma^2}\right),$$

where $I_0(z)$ is a Modified Bessel Function of the First Kind and $Z > 0$. For a derivation, see Papoulis (1962). For $\vert V\vert$ = 0, this reduces to the Rayleigh Distribution.

See also Rayleigh Distribution

References

Papoulis, A. The Fourier Integral and Its Applications. New York: McGraw-Hill, 1962.