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A problem with CDF



Hi 


	I have a problem using CDF in Mathematica.  I am trying to evaluate a
multivarivate integral with dimension >=2.  It seems to me that
Mathematica can't handle the problem well with a special correlation
matrix, sigma (m3 as follows) when dim >2, but it is working fine when
dim=2.  Is it a limitation of Mathematica? or do I overlook a mistake?


Thank you
Mark


*********************************************

In[16]:= <<Statistics`MultinormalDistribution`


In[17]:= m3=Table[If[i<=j,Sqrt[i/j],Sqrt[j/i]],{i,3},{j,3}]

                 1        1          1             2        1          2
Out[17]= {{1, -------, -------}, {-------, 1, Sqrt[-]}, {-------,
Sqrt[-], 1}}
              Sqrt[2]  Sqrt[3]    Sqrt[2]          3     Sqrt[3]       3


In[18]:= dist=MultinormalDistribution[{0, 0,0},m3]

Out[18]= MultinormalDistribution[{0, 0, 0}, 
 
             1        1          1                 1          2
>    {{1, -------, -------}, {-------, <<2>>}, {-------, Sqrt[-], 1}}]
          Sqrt[2]  Sqrt[3]    Sqrt[2]           Sqrt[3]       3

In[20]:= CDF[dist,{0,0,0}]

                                 1
Power::infy: Infinite expression - encountered.
                                 0

NIntegrate::inum: 
   Integrand 0.00603870503532375 (1. + Erf[ComplexInfinity])
     is not numerical at
{Statistics`MultinormalDistribution`Private`z$72} = 
    {-1.}.

NIntegrate::inum: 
   Integrand 0.00603870503532375 (1. + Erf[ComplexInfinity])
     is not numerical at
{Statistics`MultinormalDistribution`Private`z$72} = 
    {-1.}.

Out[20]= NIntegrate[
 
          Statistics`MultinormalDistribution`Private`product$72
>     -------------------------------------------------------------, 
                                                      2
       Statistics`MultinormalDistribution`Private`z$72 /2       1/2
      E                                                   (2 Pi)
 
>    {Statistics`MultinormalDistribution`Private`z$72, -Infinity,
Infinity}, 
 
>    AccuracyGoal ->
Statistics`MultinormalDistribution`Private`accgoal$72]


************************************************




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