Rank and Linear Correlation Differences in Monte Carlo Simulation

Abstract

Monte Carlo simulation is used to quantify and characterize uncertainty in a variety of applications, such as cost and engineering economic analysis and project management. The dependence or correlation between the random variables modeled can also be simulated to add more accuracy to simulations. However, there exists a difference between how correlation is most often estimated from data (linear correlation) and the correlation that is simulated (rank correlation). In this research an empirical methodology is developed to estimate the difference between the specified linear correlation between two random variables and the resulting linear correlation when rank correlation is simulated. It is shown that in some cases there can be relatively large differences. The methodology is based on the shape of the quantile-quantile plot of two distributions, the maximum possible linear correlation between two distributions, and the estimated level of correlation between the two random variables. This methodology also gives users the ability to estimate the rank correlation that, when simulated, generates a desired linear correlation. This methodology enhances the accuracy of simulations with dependent random variables while utilizing existing simulation software tools.