       • 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

```

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