Assuming two uncorrelated random variable (RVs) with Gaussian distributions x∼N(m1,s) and y∼N(m2,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!