Sensitivity Analysis Based on Cramér--von Mises Distance

In this paper, we first study a sensitivity index that is based on higher moments and generalizes the so-called Sobol one. Further, following an idea of Borgonovo (see [Reliab. Eng. Syst. Saf., 92 (2007), pp. 771--784]), we define and study a new sensitivity index based on the Cramér--von Mises distance. This index appears to be more general than the Sobol one as it takes into account the whole distribution of the random variable and not only the variance. Furthermore, we study the statistical properties of its pick and freeze estimator.