  Approximation and uncertainty quantification methods based on Lagrange
interpolation are typically abandoned in cases where the probability
distributions of one or more {system} parameters are not normal, uniform, or
closely related {distributions}, due to the computational issues that arise
when one wishes to define interpolation nodes for general distributions. This
paper examines the use of the recently introduced weighted Leja nodes for that
purpose. Weighted Leja interpolation rules are presented, along with a
dimension-adaptive sparse interpolation algorithm, to be employed in the case
of high-dimensional input uncertainty. The performance and reliability of the
suggested approach is verified by four numerical experiments, where the
respective models feature extreme value and truncated normal parameter
distributions. Furthermore, the suggested approach is compared with a
well-established polynomial chaos method and found to be either comparable or
superior in terms of approximation and statistics estimation accuracy.
