Re: Asymmetric quadratic coefficient problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg49877] Re: Asymmetric quadratic coefficient problem*From*: "Rob Pratt" <Rob.Pratt at sas.com>*Date*: Thu, 5 Aug 2004 09:20:39 -0400 (EDT)*Organization*: SAS*References*: <cequfb$k3m$1@smc.vnet.net>*Reply-to*: "Rob Pratt" <Rob.Pratt at sas.com>*Sender*: owner-wri-mathgroup at wolfram.com

"Xiao Huang" <xiaohda at hotmail.com> wrote in message news:cequfb$k3m$1 at smc.vnet.net... > 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 Replace your asymmetric matrix A with the symmetric matrix (A + A') / 2. Note that z'[(A + A') / 2]z = z'Az / 2 + z'A'z / 2 = z'Az / 2 + (z'Az)' / 2 = z'Az / 2 + z'Az / 2 = z'Az. Rob