Some properties of Gaussian mixtures and applications to magnetoencephalography problems

The article is dedicated to research of various properties of compound probability distributions (mixture distributions). Special attention is paid to the case when the mixed distribution is Gaussian. The authors establish the similarities in the behavior of Gaussian mixtures and Gaussian distributions during transformations. The authors study applications to magnetoencephalographic brain research. The authors determine the conditions under which the Aitken estimator (generalized least squares) is applicable for localization of sources of neurophysiologic activity in the case of noise having compound Gaussian distribution.