       Integrate the Multivariate normal distribution

• To: mathgroup at smc.vnet.net
• Subject: [mg67451] Integrate the Multivariate normal distribution
• From: "Miguel Lejeune" <mlejeune at andrew.cmu.edu>
• Date: Sun, 25 Jun 2006 03:19:18 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hello,

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?
Example:

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,

Miguel

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