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Chi or Rayleigh or Ricean?

  1. Jun 17, 2011 #1
    Hello all,

    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.
  2. jcsd
  3. Jun 17, 2011 #2
    Plz help!!
  4. Jun 17, 2011 #3
    It's a non-central chi distribution.
  5. Jun 17, 2011 #4
    For a non-central chi distribution, means can be different. But can variances be different as well? As far as I know, variances must be 1.
  6. Jun 17, 2011 #5
    Err, sorry, got a bit over-enthusiastic and thought it should fit nicely, but seems it doesn't after all, so yes looks more complicated.
  7. Jun 17, 2011 #6
    And don't think you'll get a nice analytic distribution for this. There seem to be a few numerical methods out there for managing the distribution of a linear combination of non-central chi squared random variables though, which is fairly close to what you want (apart from the square root)
  8. Jun 17, 2011 #7
    thank you so much. I'll look it up.
  9. Jun 19, 2011 #8
    How is the Z derived in the error analysis?
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