The boosted mixture learning method, BML, is an incremental method to learn mixture models for the classification prob
lem. In each step of the boosted mixture learning method, a new component is added to the mixture model according to
 an objective function to ensure that the objective function is maximized. Sometimes the likelihood function or equivalently
 information criteria are defined as the objective function of BML. The mixture model is updated whenever a new component
 is added to the mixture model based on the maximum likelihood function and information criteria. Since the information
 criteria does not have the ability to identify equivalent models, therefore, it is possible that the new mixture model and the
 current mixture model are equivalent. In this paper, the boosted mixture learning method has been corrected using Vuong’s
 model selection test, which has the ability to identify equivalent models. The performance of two learning methods is eval
uated over simulation data and over the U.S. imports of goods by customs basis.