  Input variables in numerical models are often subject to several levels of
uncertainty, usually modeled by probability distributions. In the context of
uncertainty quantification applied to these models, studying the robustness of
output quantities with respect to the input distributions requires: (a)
defining variational classes for these distributions; (b) calculating boundary
values for the output quantities of interest with respect to these variational
classes. The latter should be defined in a way that is consistent with the
information structure defined by the ``baseline'' choice of input
distributions. Considering parametric families, the variational classes are
defined using the geodesic distance in their Riemannian manifold, a generic
approach to such problems. Theoretical results and application tools are
provided to justify and facilitate the implementation of such robustness
studies, in concrete situations where these distributions are truncated -- a
setting frequently encountered in applications. The feasibility of our approach
is illustrated in a simplified industrial case study.
