Criteri ottimali e “quasi” ottimali di classificazione per caratteri continui nel caso della varianza fra i gruppi

This work presents a continuous characters classification tecnique, which satisfies some optimality criterion, such as the maximisation of the variance “between” or the minimisation of the concentration “within” the groups, measured by some index which admits a decomposition. Such a tecnique is based on an algorithm which gives all the possible frequency distributions with fixed sum, the way that each class is not empty. As the algorithm is exponential, it is necessary to impose the minimum number of statistical units per class, which fact implies the construction of two classes of residual statistical units, to the left and to the right. In order to have indications about the optimal number of classes, the minimum number of statistical units per class, and about the imputation of the residual statistical units to the left and the right class, the tecnique will be applied to classify a 13868 individual income sample, drawn by Italian Bank in 1991.