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Asymmetric quadratic coefficient problem


Dear All,

Does any one know how to deal with asymmetric quadratic coefficient in 
QuadraticFormDistribution[ {A,b,c}, {mu, sigma}] for z'Az+b'z+c?
Mathematica assumes A is a symmetric matrix, but I now have an asymmetric 
and singular matrix A.

Also, I'd really appreciate if any expert here can give me some 
clue/reference about the following problem: how can I calculate different 
quantiles of a mixture distribution? One way is to do the simulation, but is 
it possible to use the function Quantile[.] in Mathematica? if yes, how?

Thank you!

Xiao

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