Distribution of difference of two second degree non central chi squared random variables. 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!!!!