I am trying to generate random vectors with the same covariance, mean and sd as a set I have. I am using R's mvrnorm with Empirical = F because the underlying distribution is in general not normal. However when running this many times I get the impression that specific elements of the returned vectors are too similar to the original vector. Is there a way to verify this quantitatively? and if this is indeed the case, how can I generate vectors that are "completely different" from the original (while maintaining same sd and mean)?
> df A B 1 1.138289 1.918876 2 1.621082 2.432379 3 1.295929 2.241403 4 1.325516 1.845258 mvrnorm(n = 4, mu = center, Sigma = as.matrix(cov(df)), empirical = F) A B [1,] 1.364986 2.235192 [2,] 1.116274 1.828175 [3,] 1.438028 2.256231 [4,] 1.586585 1.956803
Although the bias cannot be shown from this example (but only for a large number of samples), there are pairs which are the same as the original (up to 2 digits after the decimal point), which are returned significantly more than others.