VoseCorrToCov | Vose Software


See also: Multivariate_Normal_distribution ,  VoseCovToCorr, Vose_Correlation_Matrix




Example model

The covariance between two random variables X and Y is defined as:

where E[ ] means the expected value, and X, Y refer to the respective means of X and Y.

The size of Cov(X,Y) depend on the degree to which the variables deviate from their respective means. Pearson’s correlation coefficient XY normalises the covariance to be independent of this variation, as follows:

VoseCorrToCov is an array function that combines a correlation matrix for a set of variables with a vector of standard deviation values for each variable to produce a covariance matrix. For example:

The cell range C13:G17 contains the covariance matrix. The top left to bottom right diagonal elements equal the variance (stdev^2) of each variable because XX = 1. The elements in opposite positions from the diagonal are the same, meaning that {X,Y} has the same covariance as {Y,X}.