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Integrate the Multivariate normal distribution

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  • Subject: [mg67451] Integrate the Multivariate normal distribution
  • From: "Miguel Lejeune" <mlejeune at>
  • Date: Sun, 25 Jun 2006 03:19:18 -0400 (EDT)
  • Sender: owner-wri-mathgroup at


  I am using the MultiNormal function to compute the probability density 
function (pdf_ and cumulative probability distribution (cdf) of a 
bivraite normally distributed variable.

  I have two questions.

  1) I followed the help file to get familiar with that function.
  But although I repeat what is indicated, I do not obtain the same 
output. Could you please indicate me?

  In:  Statistics`MultinormalDistribution
  In: (r = {{1, 0.2}, {0.2, 1}};
  ndist = MultinormalDistribution[{0, 0}, r])

  I obtain as output:
  Out: MultinormalDistribution [ {{0, 0}, {1, 0.2}, {1,0.2, 1}}]
  which is fine.

  However, when I type:

  In:  pdf = PDF[ndist, {x1, x2}]

  The only output I obtain is:
  MultinormalDistribution[{0, 0}, {{1, 0.2}, {1, 0, 2}}]

  while in the help file it is indicated that I should obtain an 
algebraic expression.

  Why is it??

  2) My second question. I would like to proceed to the numerical 
integration of the CDF of the bivariate normal distribution. I enter:

  In:   NIntegrate[CDF[ndist, {x1, x2}], {x1, -Infinity, 0}, {x2,-Infinity, 0}]

  I systematically obtain the following error message:

  "NIntegrate::inum: Integrand CDF[MultinormalDistribution[{0, 0}, {{1,0.5}, \
  {1, 0, 5}}], {x1, x2}] is not numerical at {x1, x2} = {-1., -1.}
  I do not understand why it is saying that the expression  is not 
numerical at {-1,1}. Could anybody help?

  Many thanks,


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