An approximate method for sampling correlated random variables from partially-specified distributions

This paper presents an algorithm for generating correlated vectors of random numbers. The user need not fully specify the joint distribution function; instead, the user ‘partially specifies’ only the marginal distributions and the correlation matrix. The algorithm may be applied to any set of continuous, strictly increasing distribution functions; the marginal distributions need not all be of the same functional form. The correlation matrix is first checked for mathematical consistency (positive semi-definiteness), and adjusted if necessary. Then the correlated random vectors are generated using a combination of Cholesky decomposition and Gauss–Newton iteration. Applications are made to cost analysis, where correlations are often present between cost elements in a work breakdown structure.