An algorithm for generating positively correlated Beta-distributed random variables with known marginal distributions and a specified correlation

A new algorithm for generating two positively correlated Beta-distributed random variables with known marginal distributions and a specified correlation is provided. The paired Beta-distributed random variables are generated from ratios of independent standard Gamma distributions. A positive correlation is achieved by introducing two shared standard Gamma distributed random variables. Parameters of the shared random variables are found by equating a one-term Taylor-series approximation of the expected covariance between the paired Beta random variables to the covariance commensurate with a specified correlation. The new algorithm is widely applicable. Upper limits of the correlation for given marginals are given. Tests of the algorithm revealed a small but persistent negative bias of 0.02 in achieved correlations. An application example is provided. (C) 2003 Published by Elsevier B.V.