Journal Article10.1080/03610918.2016.1148726
Modeling a minimal spanning tree
Haigang Liu,Reza Modarres +1 more
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TL;DR: A multivariate Gini index is defined to measure the scatter of a data cloud based on the normalized ordered IDs of the MST, using a multivariate normal copula with beta marginals and a Dirichlet distribution to obtain beta vectors.
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Abstract: We 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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Citations
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