MARGINAL DISTRIBUTIONS OF FINITE MIXTURES OF MULTIVARIATE NORMAL DISTRIBUTIONS

抄録

We give a transformation such that, for a k-dimensional finite normal mixture, the number of components and the mixing ratios are preserved on each marginal density through the transformation. Furthermore, under the only assumption of a k-dimensional finite normal mixture, we construct a one-dimensional random variable with a finite normal mixture of the true number of components and the true mixing ratios.