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MultinormalDistributions an a RobustMultinomialDistribution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg131303] MultinormalDistributions an a RobustMultinomialDistribution
  • From: J Jesus Rico-Melgoza <ricomelgozajjesus at gmail.com>
  • Date: Tue, 25 Jun 2013 21:15:09 -0400 (EDT)
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Dear members of the mathgroup

I have been working with multinormal distributions with dimensions about
24. In many cases, the covariance matrices are of deficient rank and
defining distributions via MultinormalDistribution becomes defficult. To
solve this issue I have define my own function like this

RobustMultinormalDistribution[x_, =CE=BC_, =CE=A3_] := Module[{aux, fac, d},
  d = Length[x];
  aux = 0.5 (x - =CE=BC).PseudoInverse[=CE=A3]. (x - =CE=BC) ;
  fac = (2.0 Pi)^(d/2) PseudoDet[=CE=A3]^(1/2);
  Exp[-aux]/fac
  ]
PseudoDet[a_] := Product[Eigenvalues[a][[i]], {i, 1, MatrixRank[a]}]

It works very well, I think!

However, I would like to use it in all the ways other distributions are
used with in mathematica, such as in RandomVariate and PDF functions.

Could anyone suggest how to  do function definition?
Best regards
Jesus Rico-Melgoza




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