*J. Japan Statist. Soc.,* Vol. 31 (No. 2), pp. 187-191, 2001

## Marginal Distributions of Finite Mixtures of Multivariate Normal Distributions

Jogi Henna

**Abstract. **
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.

*Key words and phrases*:
Finite mixture, *k*-dimensional distribution, One-dimensional distribution, Orthogonal matrix.

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