Uniform Test on the Mixture Simplex Region

For the symmetrical mixture model and mixture test area, the lattice point set is used to partition, and then the corresponding test statistics can be constructed. In this paper, we first proposes the partition methods under the lattice point sets and obtains several sub-simplexes without common interior points. Furthermore, we present the method for constructing a uniform design on the simplex using the center points of these sub-simplexes. The designs satisfy the uniformity of maximum distance deviation and provide good results for the mean square error deviation. Finally, the uniformity test on the mixture region is considered and illustrated by examples.