  The impact of the third (skewness) and fourth (kurtosis) reduced centered
moments on the statistical modeling of E1 lines in complex atomic spectra is
investigated through the use of Gram-Charlier, Normal Inverse Gaussian and
Generalized Gaussian distributions. It is shown that the modeling of unresolved
transition arrays with non-Gaussian distributions may reveal more detailed
structures, due essentially to the large value of the kurtosis. In the present
work, focus is put essentially on the Generalized Gaussian, the power of the
argument in the exponential being constrained by the kurtosis value. The
relevance of the new statistical line distribution is checked by comparisons
with smoothed detailed line-by-line calculations and through the analysis of
2p-3d transitions of recent laser or Z-pinch absorption measurements. The issue
of calculating high-order moments is also discussed (Racah algebra, Jucys
graphical method, semi-empirical approach ...).
