Abstract
ABSTRACTWe model the distribution of the normalized interpoint distances (IDs) on the minimal spanning tree (MST) using multivariate beta vectors. We use a multivariate normal copula with beta marginals and a Dirichlet distribution to obtain beta vectors. Based on the normalized ordered IDs of the MST, we define a multivariate Gini index to measure the scatter of a data cloud. An example considers the MST of numerals in 11 European languages and obtains their Gini index. A simulation study compares the Gini index, the maximum and the range of the IDs for multivariate normal and log-normal data, with the results of modeling the distances on the MST.
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