A distribution-free approach to inducing rank correlation among input variables

TLDR

The paper introduces a method to induce a specified rank correlation matrix in multivariate input variables for simulation studies. The method is simple, distribution‑free, preserves marginal distributions, and works with any sampling scheme that requires input variable correlation. Monte Carlo experiments estimate the bias and variability of the method, and examples from a radioactive‑waste disposal model and a textbook case illustrate its impact on outputs.

Abstract

A method for inducing a desired rank correlation matrix on a multivariate input random variable for use in a simulation study is introduced in this paper. This method is simple to use, is distribution free, preserves the exact form of the marginal distributions on the input variables, and may be used with any type of sampling scheme for which correlation of input variables is a meaningful concept. A Monte Carlo study provides an estimate of the bias and variability associated with the method. Input variables used in a model for study of geologic disposal of radioactive waste provide an example of the usefulness of this procedure. A textbook example shows how the output may be affected by the method presented in this paper.