Distribution of Sum of F distributed rv?

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The discussion centers on determining the distribution of the sum of n F-distributed random variables and n non-central F-distributed random variables. It suggests that to find the joint distribution, one must specify values for the integral of each cumulative distribution function (CDF) and utilize characteristic functions. References provided include a link to MathWorld for F-distribution details and a book that discusses multivariate joint F-distributions. Understanding these distributions is crucial for statistical analysis involving F-distributed variables. The conversation emphasizes the need for further exploration of these mathematical concepts.
saaagar10
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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!
 
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saaagar10 said:
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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