  In the paper there is given a connection between one special case of cluster
analysis, deconvolution problem, and classical moment problem. Namely, the
methods used there are applied to solve deconvolution problem for the case of
one known distribution and another one concentrated in unknown finite number of
points. These results can be applied to estimate a number of clusters for the
case of scale or location mixture of identical distributions.
  keywords: number of clusters, deconvolution problem, classical moment
problem, scale and location mixtures.
