# Sum of non-identical non-central Chi-square random variables.

1. Jan 30, 2012

### no999

Hi All,

By definition, the sum of iid non-central chi-square RVs is non-central chi-square. what is the sum of ono-identical non-central chi-square RV.

I have a set of non zero mean complex Gaussian random variables H_i with a mean m_i and variance σ_i . i=1...N. H
the result of their square is non-central chi-square RM. Now what is the distribution of the sum of those non-central chi-square RV given that their variances are different "i.e., they are independent but non-identical distributed".

Kind Regards

2. Dec 7, 2014

### kdl05

I am also very much interested in the answer. Anyone know the answer??

Thanks

3. Dec 15, 2014

### DrDu

It is easy to write down an expression for the distribution, e.g. using the characteristic functions of the individual distributions.

kdl05, this is quite an old thread. Hence it would be useful if you could specify the question you are interested in. So if $X_i~N(\mu_i,\sigma_i)$, the original poster seemed to be intereste in the distribution of $\sum_i X_i^2$, which is not distributed as a non-central chi square. What is chi square distributed is $\sum_i (X_i/\sigma_i)^2$.

Last edited: Dec 15, 2014