The asymptotic joint normality of the numbers of upper records, lower records and inversions in a random sequence

We describe an algorithm to obtain additive trees based upon the preservation of the clusters structure and the minimization of the stress measure between the additive distance and the best linear combination of the initial dissimilarity. For the proposed method we introduce a hypothesis test to evaluate the statistical significance of the additive structure and perform a first simulation study to evaluate the percentage reduction in stress.