  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.
