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What is the PDF of the sum of n, iid, non central chi-square

  1. Mar 8, 2017 #1
    1. The problem statement, all variables and given/known data
    I need to find the pdf of sum of "n" iid non central chi-square distributed RV's.

    2. Relevant equations
    The PDF of the non-central chi-square RV is given herehttps://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution

    3. The attempt at a solution
    i tried to find the product of the characteristics function of "n" RV, but how to continue?
     
    Last edited: Mar 8, 2017
  2. jcsd
  3. Mar 8, 2017 #2

    Ray Vickson

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    Why not use the moment-generating function instead?
     
  4. Mar 8, 2017 #3
    I'm new to this and i'm learning the basics now. In addition, i have noticed someone who suggested to start with the characteristic function.Can you give the way to do it using the MGF?
     
  5. Mar 8, 2017 #4

    Ray Vickson

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    The MGF of a sum of independent RVs is the product of their MGFs---the same as it is for characteristic functions or Laplace transforms.
     
  6. Mar 8, 2017 #5
    Okay..but after we find the characteristic function or the MGF of their product...what does the resulted formula indicates? That's what i need to know...how is this formula related to the pdf of the sum of these random variables?
     
  7. Mar 8, 2017 #6

    Ray Vickson

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    I suggest you answer that question for yourself, by first writing out the details for the sum of 2 iid ##X##s.

    Another way to solve the problem is to go right back to the beginning: what is the random variable that has the non-central chi-squared distribution? How is it related to the normal distribution? Answering that allows a simple solution almost by inspection and without any calculations at all!
     
  8. Mar 8, 2017 #7
    I started from here https://www.physicsforums.com/threads/sum-of-noncentral-chi-square-rvs.374004/ , a homework helper "statdad" has suggested the method and i followed him, i did find the CF of the multiplication of the RV's CF, i just need to know how to continue.
     
  9. Mar 8, 2017 #8

    Ray Vickson

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