  We study an industrial computer code related to nuclear safety. A major topic
of interest is to assess the uncertainties tainting the results of a computer
simulation. In this work we gain robustness on the quantification of a risk
measurement by accounting for all sources of uncertainties tainting the inputs
of a computer code. To that extent, we evaluate the maximum quantile over a
class of distributions defined only by constraints on their moments. Two
options are available when dealing with such complex optimization problems: one
can either optimize under constraints; or preferably, one should reformulate
the objective function. We identify a well suited parameterization to compute
the optimal quantile based on the theory of canonical moments. It allows an
effective, free of constraints, optimization.
