[R] big difference in estimate between dmvnorm and dnorm, how come?

saverio vicario saverio.vicario at yale.edu
Fri Jan 20 16:30:44 CET 2006

```Dear R community,
I was trying to estimate density at point zero of a multivariate
distribution (9 dimensions) and for this I was using a multinormal
approximation and the function dmvnorm , gtools package.
To have a sense of the error I tried to look the mismatch between a
unidimensional version of my distribution and estimate density at
point zero with function density, dmvnorm and dnorm.
At my big surprise dmvnorm and dnorm give very different result and
dmvnorm match even better the theoritical distribution than the
function density. How come?

#sampling from triangular distribution
X<-runif(10000)- runif(10000)
X<-matrix(X,length(X),1)

#dnorm estimate
plot(-100:100/100, dnorm((-100:100)/100,mean(X),var(X)),col=2,type="l")
#kernel density estimate
lines(density(X))
#dmvnorm estimate
res<-rep(NA,201);for ( i in
-100:100){res[i+101]<-dmvnorm(i/100,mean(X),var(X))}
lines(-100:100/100, res,col=3)
#Theoretic triangular distribution
lines(-1:1,c(0,1,0),col=4)

```