[R] A question about multivariate normal distribution with a diagonal covariance matrix

[Duncan Murdoch]

On 29/08/2013 1:37 PM, Marino David wrote:
> Hi all R users:
>
>
>
> I am a little bit confused about the following results. See as follows:
>
>
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> library(mvtnorm)
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>
>
> xMean<-c(24.12,66.92,77.65,131.97,158.8)
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> xVar<-c(0.01,0.06,0.32,0.18,0.95)
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> xFloor<-floor(xMean)
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>
>
> # use “mvtnorm” package
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> p1<-dmvnorm(xFloor,mean=xMean,sigma=diag(xVar))
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> p2<-dmvnorm(xFloor[1],mean=xMean[1],sigma=matrix(xVar[1]))*dmvnorm(xFloor[2],mean=xMean[2],sigma=matrix(xVar[2]))*dmvnorm(xFloor[3],mean=xMean[3],sigma=matrix(xVar[3]))
>
>
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> # use the basic package “stats”
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> p3<-dnorm(xFloor[1],mean=xMean[1],sd=sqrt(xVar[1]))*dnorm(xFloor[2],mean=xMean[2],sd=sqrt(xVar[2]))*dnorm(xFloor[3],mean=xMean[3],sd=sqrt(xVar[3]))
>
>
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> The result is: p1= 2.006403e-05, p2=p3= 0.00099646. My question is why p1
> does not equal to p2 when the covariance matrix is diagonal, meaning no
> correlation among variates. From p2=p3, it seems that the “mvtnorm” package
> exhibits well agreement with the R basic package. Any explain will be
> greatly appreciated.
>

Why would you expect p1=p2? p1 is the density in 5 dimensions, p2 is 
only the first 3 components.

Duncan Murdoch