A Multivariate Quantile Based on Kendall Ordering
Accepted - September 2021
Keywords:multivariate quantile, copula, Archimedean copula, Kendall distribution, orthant quantile
We introduce the Kendall multivariate quantiles, which are a transformation of orthant quantiles by the Kendall function. Each quantile is then a set of vectors with some advantageous properties, compared to the standard orthant quantile: i/ it induces a total order, ii/ the probability level of the quantile is consistent with the probability measure of the set of the dominated vectors, iii/ the multivariate quantiles based on the distribution function or on the survival function have vectors in common which conciliate both upper- and lower-orthant approaches. Definition and properties of the Kendall multivariate quantiles are illustrated using Archimedean copulas.
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