Some descriptive properties of normal mixtures

Abstract

Abstract When two single normal densities are mixed together the shape of the resulting distribution will vary in the extent to which it indicates the underlying structure, depending on the values of the parameters. It does not seem unreasonable to suppose that the more the mixing structure is revealed the more accurately can the density be estimated in practice. For this reason it is important to identify the regions in the parameter space where the prospects are most favourable. An examination of the total parameter space is also a pre-requisite for an assessment of the efficiencies of various methods of estimation for the mixture. This is so since it is necessary to select regions of the parameter space where the methods are to be compared and essential to know the population implications of these regions.