On Modelling Human Population Characteristics with Copulas

Copulas are fast gaining in popularity in fields requiring modelling of multivariate data. Population synthesis is one such domain where copulas hold much promise. Characteristics of a population are inherently a multivariate distribution, for example, age, education and employment have a dependent relationship with each other. However, characteristics of population are often discrete, sometimes even categorical, and rarely continuous. Further, inherently continuous variables like age are often discretized into bins or rounded down to the nearest integer. Although the Sklar’s representation theorem of copulas [23] is still valid for these discrete data, assessing the goodness of fit by rejecting the null hypothesis that an assumed family of copulas adequately represents the data may not be fool-proof. In this paper, through simulation we demonstrate the failure of accepted goodness of fit tests of copulas even when the copula family is able to capture the dependence in the data. The strong recommendation is to use additional methods to test that the copula can capture the dependence in the available data.