L. G. M. de Souza for helpful discussions on the topic of probability reconstruction from moments.

Appendix {#appendix .unnumbered}
========

In Table \[tab:chi2\] values of the negative base ten logarithm of $\chi^2$ rounded down to the first digit (defined in Eq. (\[eqn:chisquared\])) is shown for the reconstructed probabilities in Figs. \[fig:prob\] and \[fig:prob1\]. In all cases $\chi^2$ decreased at least eight orders of magnitude from its initial value during the simulated annealing calculation.

In Table \[tab:chi2\_circles\] the values of the parameters according to the parametrization used in Figs. \[fig:mom01\]-\[fig:prob1\] are shown. Also shown are values of the negative base ten logarithm of $\chi^2$ rounded down to the first digit for probability distributions corresponding to the points in Figs. \[fig:CircleR1\] and \[fig:CircleR02\].

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