Hi all R users:



I am a little bit confused about the following results. See as follows:



library(mvtnorm)



xMean<-c(24.12,66.92,77.65,131.97,158.8)

xVar<-c(0.01,0.06,0.32,0.18,0.95)

xFloor<-floor(xMean)



# use “mvtnorm” package

p1<-dmvnorm(xFloor,mean=xMean,sigma=diag(xVar))

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]))



# use the basic package “stats”

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]))



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.



Thanks in advance!



David

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