Limiting distributions of high-dimensional multivariate Beta-type distributions

This paper investigates the limiting distributions of two high-dimensional multivariate Beta-type distributions. These Beta distributions have three parameters including a dimension. Limiting distributions of the Beta distributions have been obtained under one or two parameters that tend toward infinity. In this paper, we derive the limiting distributions of two multivariate Beta-type distributions under three parameters that tend toward infinity. These results were obtained using the martingale limit theory. Numerical simulations revealed that those approximations are more accurate than the other approximations for a wide range.