On separation of a set of vectors into two classes

A mixture of sampled values of two random vectors with unknown distributions and different means in to be separated. The vector is $\mathbf{\alpha}$ whose $i$-th component is either 1 or 0 depending on whether the $i$-th sampled value is a member in the one or the other distribution. The dependence is determined of $\mathbf{\alpha}$ on unknown means and on the number of sampled values in either distribution. An estimate of $\mathbf{\alpha}$ obtained by replacing the unknown means with sampled values is used for separation of the mixture. The efficiency of the method is illustrated with model examples.