Relaxing the multivariate normality assumption in the simulation of transportation system dependencies: an old technique in a new domain

Abstract

By far the most popular method to account for dependencies in the transportation network analysis literature is the use of the multivariate normal (MVN) distribution. While in certain cases there is some theoretical underpinning for the MVN assumption, in others there is none. This can lead to misleading results: results do not only depend on <i>whether</i> dependence is modeled, but also <i>how</i> dependence is modeled. When assuming the MVN distribution, one is limiting oneself to a specific set of dependency structures, which can substantially limit validity of results. In this paper an existing, more flexible, correlation-based approach (where just marginal distributions and their correlations are specified) is proposed, and it is demonstrated that, in simulation studies, such an approach is a generalization of the MVN assumption. The need for such generalization is particularly critical in the transportation network modeling literature, where oftentimes there exists no or insufficient data to estimate probability distributions, so that sensitivity analyses assuming different dependence structures could be extremely valuable. However, the proposed method has its own drawbacks. For example, it is again not able to exhaust all possible dependence forms and it relies on some not-so-known properties of the correlation coefficient.

Keywords:

• dependence
• correlation
• simulation
• multivariate normal distribution
• stochastic transportation networks