  At present, it is still unknown whether the correct mass ordering of the
neutrino mass eigenstates is either $m_1$, $m_2$, $m_3$ (Normal Hierarchy, NH),
or $m_3$, $m_1$, $m_2$ (Inverted Hierarchy, IH). The new analysis method
proposed by Stanco et al. (arXiv:1707.07651v3) should fix some issues of the
currently most used estimator, $\Delta \chi^2$, and make it possible to reach
$5\,\sigma$ measurements in less than six years of data taking with JUNO
(Jiangmen Underground Neutrino Observatory) if a degeneracy in the atmospheric
mass, $\Delta m^2_{atm}$, is accepted. In this note, the analysis introduced in
the paper above was extended to more detailed studies on the dependence of the
new F estimator to $\Delta m^2_{atm}$. A fit to the values of the new estimator
as a function of $\Delta m^2_{atm}$, calculated for both the true hierarchy and
the wrong hierarchy, was performed. The study of the fitting function showed
that the average minimum counts, corresponding to the best value for $\Delta
m^2_{atm}$, either for the true hierarchy or for the wrong hierarchy, are well
separated, and allow to distinguish easily between NH and IH.
