Distribution of difference of two second degree non central chi squared random variables.(adsbygoogle = window.adsbygoogle || []).push({});

This problem can be cast as an indefinite quadratic form for which there are a number of general numerical techniques to determine the CDF. Alternatively, it may be written as a linear combination of independent chi squared random variables.

I'm wondering if there are any simplifications when the linear combination takes the form

of a simple difference of two second degree non-central chi squared distributions.

Context: Consider a two dimensional complex normal random vector x = [x1 x2]' ~ CN(u,R).

I am interested in the distribution of:

|x1|^2 - |x2|^2

Thanks!!!!

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# Distribution of difference of 2 2nd degree non central chi squared random variables

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