Estimating Location Parameters in a Mixture Model

Mixture models of the form h = sum to M terms, one for each positive integer from 1 to N lambda sub j f (j) sub theta sub j where theta sub j is a translation parameter are considered. An approach is discussed which makes use of a Caratheodory theorem on the trigonometric moment problem to determine M and theta sub j j = 1,2,...,M. This theorem is also applied to show that translates of many common distributions lead to identifiable mixtures.