As the global health community prioritizes reducing the global burden of child growth failure (stunting, underweight, and wasting [CGF]) in the next decade, comprehensive estimation of CGF should consider the joint distributions of these conditions, as by definition the burden of one is connected to the burden of the others. This study uses anthropometric data from 618 population surveys to assess the marginal distributions of the CGF indicators, the copulas that connect the joint distributions of those indicators, and the difference in CGF prevalence between empirical and simulated joint distributions. The results show that a single distribution and copula family cannot be used to describe the different age-sex patterns of the joint distributions of CGF. Future joint distribution CGF analyses should incorporate these results and iterate on the analyzed distributions to improve simulation of the joint distribution of CGF.