After presenting a short review of random-projection techniques, we address two important statistical problems: that of estimating for mixtures of multivariate normal distributions and mixtures of $t$-distributions based of univariate projections, and that of measuring the agreement between two different random partitions. The results are based on an earlier work of the authors, where it was shown that mixtures of multivariate Gaussian or $t$-distributions can be distinguished by projecting them onto a certain predetermined finite set of lines, the number of lines depending only on the total number of distributions involved and on the ambient dimension. We also compare our proposal with robust versions of the expectation-maximization method EM. In each case, we present algorithms for effecting the task, and compare them with existing methods by carrying out some simulations.

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