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Monte Carlo Analysis
Correlation Between Gaussian Input Variables
The correlation coefficient has a similar interpretation to the covariance, but is such that
-1≤ρ(X,Y)≤1. For independent random variables, the correlation is zero. The converse is false,
as the correlation is a measure only of the extent to which variables are linearly associated.
Consequently, variables may have zero correlation if their association is non-linear.
Figure 11-8. Scatter Plot of a Gaussian Sample and Contour Ellipses
For a general random vector X = (X 1 , …, X k ) T , it is usual to pack together all the information on
variances and covariances between each pair of variables into matrix, the variance-covariance
matrix, defined as:
where and for .
Eldo® User's Manual, 15.3 439