Mixture Decomposition of Distributions by Copulas
Each unit is described by a vector of p distributions each one associated to one of p variables. Our aim is to find simultaneously a “good” partition of these units and a model using “copulas” associated to each class of this partition. Different copulas models are recalled. The mixture decomposition problem is settled in this general case. It extends the standard mixture decomposition problem to the case where each unit is described by a vector of distributions instead as usual, by a vector of a single (categorical or numerical) values. Several generalization of standard algorithms are suggested. All these results are first considered in the case of a single variable and then extended to the case of a vector of p variables by using a top-down binary tree approach.
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