The modeling of dependence between maxima is an important subject in several applications in risk analysis.To this aim, the extreme value copula function, characterised via the madogram, can be used as a margin-free description of the dependence structure. From a practical point of view, the family of extreme value distributions is very rich and arise naturally as the limiting distribution of properly normalised component-wise maxima. In this paper, we investigate the nonparametric estimation of the madogram where data are completely missing at random. We provide the functional central limit theorem for the considered multivariate madrogram correctly normalized, towards a tight Gaussian process for which the covariance function depends on the probabilities of missing. Explicit formula for the asymptotic variance is also given. Our results are illustrated in a finite sample setting with a simulation study.

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The modeling of dependence between random variables is an important subject in several applied fields of science. To this aim the copula function can be used as a margin-free description of the dependence structure. Several copulae belong to specific families such as Archimedean, Elliptical or Extreme. While software implementation of copulae has been thoroughly explored in R software, methods to work with copula in Python are still in their infancy. To promote the dependence modeling with copula in Python, we have developed COPPY, a library that provides a range of random vector generation vector for copulae.