Difference between Rician distribution and Gaussian distribution


This Wikipedia article begins as follows:

In probability theory, the Rice distribution or 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.

That should make clear that they're two different things. The normal (or "Guassian") distribution has as its support the whole real line, whereas the distribution of magnitudes of any random vector has to be supported within the half-line $[0,\infty)$. And if you look at these graphs of densities, you see that (as the above statement would lead you to think) they are asymmetric, unlike normal (i.e. "Gaussian") distributions, which are symmetric:



Related videos on Youtube

Author by


Updated on May 16, 2020


  • Tom
    Tom over 3 years

    could any one please tell me the difference between Rician and Gaussian Distribution and the advantages of using one over other please.With some mathematical proof would be truly appreciated Thank you.

    • Tim
      Tim over 10 years
      I think Rice distributions are used quite rarely, could you add more background please. You would need a very good reason to use a Rice distribution, but Gaussians are pretty much general purpose.
    • Alex Kocurek
      Alex Kocurek over 10 years
      This probably shouldn't be tagged with "logic"...