thirdOrderLossFunction

G3(x) = (1/6) * Emax(X - x, 0) * max(X - x - 1, 0) * max(X - x - 2, 0), in the third factorial moment form, matching secondOrderLossFunction.

At x = 0 this is mu^3 / 6, the third binomial moment of a Poisson. The closed form holds at negative whole numbers as well, so unlike the lower orders it needs no separate branch there: the complementary distribution function is 1 below the support and the expression collapses to the third moment about x.

A non-whole argument is interpolated exactly from the neighbouring whole numbers. The closed form cannot be used there — its complementary distribution functions are flat between integers, so it would silently return the value at the floor.