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Due to limited computational power, performing uncertainty quantificationanalyses with complex computational models can be a challenging task. This isexacerbated in the context of stochastic simulators, the response of which to agiven set of input parameters, rather than being a deterministic value, is arandom variable with unknown probability density function (PDF). Of interest inthis paper is the construction of a surrogate that can accurately predict thisresponse PDF for any input parameters. We suggest using a flexible distributionfamily -- the generalized lambda distribution -- to approximate the responsePDF. The associated distribution parameters are cast as functions of inputparameters and represented by sparse polynomial chaos expansions. To build sucha surrogate model, we propose an approach based on a local inference of theresponse PDF at each point of the experimental design based on replicated modelevaluations. Two versions of this framework are proposed and compared onanalytical examples and case studies.

Replication-based emulation of the response distribution of stochastic simulators using generalized lambda distributions