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

1. Mar 8, 2017

### deema_master

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. Mar 8, 2017

### Ray Vickson

Why not use the moment-generating function instead?

3. Mar 8, 2017

### deema_master

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?

4. Mar 8, 2017

### Ray Vickson

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.

5. Mar 8, 2017

### deema_master

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?

6. Mar 8, 2017

### Ray Vickson

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!

7. Mar 8, 2017

### deema_master

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.

8. Mar 8, 2017