2
$\begingroup$

Assuming two uncorrelated random variable (RVs) with Gaussian distributions $x\sim N(m_1,s)$ and $y\sim N(m_2,s)$, so with non-zero mean and same variance, what is the distribution of $z=\sqrt{(x^2 + y^2)}$? Is there a known parametric distribution for z?

I have already researched this problem, but I am not sure whether z is a Rician distributed RV. It has been proven that z is Ricianly distributed only when x OR y have a zero mean, because they are considered to be circular bivariate RVS in these demonstrations. I would like to know if the Ricean distribution holds when BOTH uncorrelated Gaussian RVs x and y have non-zero means.

All ideas are welcome! Thank you!

  • 0
    A [similar question](http://stats.stackexchange.com/q/9220/6633) is being discussed on stats.SE right now2012-03-26
  • 0
    The title does not describe the question.2013-02-28
  • 0
    The question omits information on the joint distribution, saying only that they are Gaussian and uncorrelated. I can show you pairs of uncorrelated Gaussians that are nowhere near being bivariate Gaussian. If they're bivariate Gaussian and uncorrelated, then they're actually independent.2013-09-13

1 Answers 1