New Fréchet features for random distributions and associated sensitivity indices

Jean-Claude Fort (1) , Thierry Klein (2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 IMT - Institut de Mathématiques de Toulouse UMR5219

In this article we define new Fréchet features for random cumulative distribution functions using contrast. These contrasts allow to construct Wasserstein costs and our new features minimize the average costs as the Fréchet mean minimizes the mean square Wasserstein2 distance. An example of new features is the median, and more generally the quantiles. From these definitions, we are able to define sensitivity indices when the random distribution is the output of a stochastic code. Associated to the Fréchet mean we extend the Sobol indices, and in general the indices associated to a contrast that we previously proposed.

Mots clés: contrats; Wassertein costs; sensitivity index

Domaines: Statistiques [stat]

Jean-Claude Fort, Thierry Klein. New Fréchet features for random distributions and associated sensitivity indices. 2015. ⟨hal-01137577⟩