  Stochastic simulators are ubiquitous in many fields of applied sciences and
engineering. In the context of uncertainty quantification and optimization, a
large number of simulations is usually necessary, which becomes intractable for
high-fidelity models. Thus surrogate models of stochastic simulators have been
intensively investigated in the last decade. In this paper, we present a novel
approach to surrogating the response distribution of a stochastic simulator
which uses generalized lambda distributions, whose parameters are represented
by polynomial chaos expansions of the model inputs. As opposed to most existing
approaches, this new method does not require replicated runs of the simulator
at each point of the experimental design. We propose a new fitting procedure
which combines maximum conditional likelihood estimation with (modified)
feasible generalized least-squares. We compare our method with state-of-the-art
nonparametric kernel estimation on four different applications stemming from
mathematical finance and epidemiology. Its performance is illustrated in terms
of the accuracy of both the mean/variance of the stochastic simulator and the
response distribution. As the proposed approach can also be used with
experimental designs containing replications, we carry out a comparison on two
of the examples, showing that replications do not necessarily help to get a
better overall accuracy and may even worsen the results (at a fixed total
number of runs of the simulator).
