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arXiv · 1503.08844

New Fr\'echet features for random distributions and associated sensitivity indices

Jean-Claude Fort·Thierry Klein
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Abstract

In this article we define new Fr\`Echet 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 Fr\`Echet mean minimizes the mean square Wasserstein$_2$ 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 Fr\`Echet mean we extend the Sobol indices, and in general the indices associated to a contrast that we previously proposed.

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Jean-Claude Fort, Thierry Klein. 2015-03-30. New Fr\'echet features for random distributions and associated sensitivity indices. https://arxiv.org/abs/1503.08844

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