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I've been working on error analysis of the system, and I finally faced a big problem.

Let X~N(mu1, sigma1^2) and Y~N(mu2, sigma2^2), and Z=sqrt( X^2 + Y^2 )

For Z to be a Chi, mu's should be zero and sigma's should be 1, to be a Rayleigh, mu's should be zero and two sigma's should be the same, and finally to be a Ricean, mu's can be different from each other, but two sigma's should be the same.

Yes, that's all I know. But in my case, mu's are different and sigma's are different as well. In this case, what is 'Z'?

I appreciated it in advance.

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# Chi or Rayleigh or Ricean?

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