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In this talk I will show some preliminary work on the inference of mass composition of Ultra High-Energy Cosmic Rays (UHECR), cosmic rays with energies $E > 10^{18}$ GeV. The composition is still hardly known: data on EM peak radiation, $X_{{\rm max}}$, suggest that the ions heavier then hydrogen dominate at higher energies, and fits with small mixture tend to confirm this. However, extracting information from the available data is not an easy task.
In this work we take a parallel path, and try to infer the full composition by decomposing the distribution of the simulated $X_{{\rm max}}$ in a series of moments, which we then fit to observed data. We infer the composition and comment on results obtained by using different high energy hadronic models in the simulations.