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MathGroup Archive 2000

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problem with QuadraticFormDistribution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24471] problem with QuadraticFormDistribution
  • From: Mark Fisher <me.fisher at atl.frb.org>
  • Date: Wed, 19 Jul 2000 01:21:48 -0400 (EDT)
  • Organization: Federal Reserve Bank of Atlanta
  • Sender: owner-wri-mathgroup at wolfram.com

There seems to be a problem with the analytical expression for the
variance of a quadratic form. I've sent this to support at wolfram.com. Any
ideas?

In[16]:=
Needs["Statistics`MultinormalDistribution`"]

In[19]:=
Q = IdentityMatrix[2];
V = {{1, 1/2}, {1/2, 1}};
M = {1, 1};

In[18]:=
qdf = QuadraticFormDistribution[{Q, {0, 0}, 0}, {M, V}];

In[23]:=
{Mean[qfd], Tr[Q.V] + M.Q.M}

Out[23]=
{4, 4}

In[24]:=
{Variance[qfd], 2 Tr[Q.V.Q.V] + 4 M.Q.V.Q.M }

Out[24]=
{41, 17}

In[32]:=
Variance[RandomArray[qdf, 10000]]

Out[32]=
16.5661

In[27]:=
Variance[#.Q.# & /@ RandomArray[MultinormalDistribution[M, V], 10000]]

Out[27]=
17.1616

--Mark.

Mark Fisher
Economic Advisor
Research Department
Federal Reserve Bank of Atlanta
Atlanta, GA 30303
404-521-8757 (voice)
404-521-8810 (fax)
mark.fisher at atl.frb.org


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