# Distribution of Sum of F distributed rv?

## Main Question or Discussion Point

Dear Good people,
I needed a help,
1. what will be the distribution of sum of n F distributed random variables?
2. what will be the distribution of sum of n non-central F distributed random variables?
Great if u can suggest some references too!
Thanks in advance!

## Answers and Replies

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Dear Good people,
I needed a help,
1. what will be the distribution of sum of n F distributed random variables?
2. what will be the distribution of sum of n non-central F distributed random variables?
Great if u can suggest some references too!
Thanks in advance!
Are you asking for the joint distribution of the CDFs of a set of F distributions?:

$$F_{m_i,n_i}=\frac{\chi_{m_i}^2/m_i}{\chi_{n_i}^2/n_i}$$.

For m and n degrees of freedom.

First you would need to specify some $$x_i$$ for the integral of each CDF and then use the characteristic functions to obtain the joint distribution function.

http://mathworld.wolfram.com/F-Distribution.html

This may also help:

http://books.google.com/books?id=vt...e&q=Multivariate Joint F distribution&f=false

see d) p 104

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