       Re: Multinormal CDF and Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg14637] Re: Multinormal CDF and Mathematica
• From: Brian Boonstra <boonstb at cmg.FCNBD.COM>
• Date: Wed, 4 Nov 1998 13:47:05 -0500
• References: <v04020a04b264a47c90f8@[24.192.58.10]>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Colin

Good grief!  You are perfectly right, of course.  I just assumed the
identity matrix case (which I was actually just using to test my
understanding of the syntax) would work the same as the general case.

Testing with a nontrivial covariance matrix shows that the CDF[]
implementation works just fine.  Thanks for your reply - it was a big
help!

Best Regards,

Brian

> > Has anyone got a fix for the (apparent) bug in the standard stats
> > package that keeps the CDF of the multivariate normal distribution from
> > being computed in 3 and more dimensions?  I find the following:

> > In:=   <<Statistics`MultinormalDistribution`

> > In:=   CDF[MultinormalDistribution[{0,0},IdentityMatrix],{0,0}]
> > Out=   0.25

> > In:=   CDF[MultinormalDistribution[{0,0,0},IdentityMatrix],{0,0,0}]
> > Solve::svars:
> > Equations may not give solutions for all "solve" variables.
>
>
>  The CDF function in the Multinormal package does not work
>  if any of the correlation coefficients is zero,
>  irrespective of whether the 0 is a symbolic zero (0) or
>  a numerical zero (0.).  Since your variance-covariance
>  matrix is an identity matrix, it doesn't work in your
>  case.
>
>  Fortunately, a FIX is easy:
>
>    In the case of zero correlation (your scenario), the
>    CDF has an easy symbolic form. For the general
>    m-dimensional case:
>
>      CDF(xvec) = (1/2)^m  (1+Erf[x1/Sqrt) *...*
>      (1+Erf[xm/Sqrt)
>
>      where xvec = {x1, x2, ..., xm}
>
>  Cheerio
>
>  Colin
>
>  Colin Rose tr(I)    -  Theoretical Research Institute

```

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