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This work deals with a clustering method for distributional data. The set of objects to be clustered are described by p distributional variables. Each object is represented by p probability functions, or empirical ones.In consideration of the most recent developments in distributional data analysis (DDA), we introduce a transformation of the qf's in Logarithm Derivative Quantiles (LDQ) functions, which allows to map density functions in an Hilbert space. Our proposal is based on a Dynamic Clustering Clustering type-algorithm, where the centroid of the clusters are represented by linear combination of LDQ functions; the objects are assigned to the clusters according to minimum sum of the squared distance from the centroid function. Applications on synthetic and real data have corroborated the new method.