Identifying The Number Of Mixture Components With Constraint Condition

The use of mixture models dates back to at least 1800, Karl Pearson used normal mixture distributions to model the mixing of different species,which motivated extensive use of mixture distributions in other application fields.When finite models are used to fit data,it is important to estimate the number of mixture components.For example,such groups may be determined by the distinct genotypes in the population,and the number of genotypes may be of primary interest.In a fish population,the size distribution depends on the age in years of the fish,we want to know to which age are the fish belong . Estimating the number of the components is the primary thing to the finite mixture models.In this paper,we mainly discuss estimating and testing of finite mixture models,and also discriminate to which component does the sample belong.