Mixing of multiple distinct components controls the behavior of many engineered and geophysical systems. For example, the rate of heat release in combustion devices is controlled by mixing of fuel, oxidizer, combustion products, and intermediate species. The spread of pollutants in the atmosphere is also a manifestation of multicomponent turbulent mixing. Turbulent flow in these systems greatly enhances the rate of mixing, but also makes prediction of the detailed mixing process more challenging because the turbulent eddies that enhance mixing are chaotic and occur across a wide range of physical length scales. A more tractable approach is to treat turbulent mixing as a statistical process and develop a model for the distribution of mixing states present in a system as a function of low-order statistical moments of the mixture fractions of each component. This work shows simulations of turbulent mixing used to test such statistical models.