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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".

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

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