1. Classic kurtosis estimation requires [0..4] moments for estimation, but 3-point Gaussian quadrature requires [0..5] moments. In this sense quadrature-based skewness estimation is some kind special, because it can be built using the same input moments as classically defined skewness. In practical applications the Christoffel function (23) asymptotic 1/K(x, x, �) can be much more successfully, than kurtosis, applied for testing a distribution on "fat tails". Technically Christoffel function behavior can be better understood in the (B1) eigenfunctions basis (in which K(x, y, �) has a very simple form (B2)) rather than in the original Q k (x) basis;While quadratures approach can be easily applied to skewness estimation, kurtosis estimain classic definition of kurtosis