  The information of the event-by-event fluctuations is extracted from flow
harmonic distributions and cumulants, which can be done experimentally. In this
work, we employ the standard method of Gram-Charlier series with the normal
kernel to find such distribution, which is the generalization of recently
introduced flow distributions for the studies of the event-by-event
fluctuations. Also, we introduce a new set of cumulants $j_n\{2k\}$ which have
more information about the fluctuations compared with other known cumulants.
The experimental data imply that not only all of the information about the
event-by-event fluctuations of collision zone properties and different stages
of the heavy-ion process are not encoded in the radial flow distribution
$p(v_n)$, but also the observables describing harmonic flows can generally be
given by the joint distribution $\mathcal{P}(v_1,v_2,...)$. In such a way, we
first introduce a set of joint cumulants $\mathcal{K}_{nm}$, and then we find
the flow joint distribution using these joint cumulants. Finally, we show that
the Symmetric Cumulants $SC(2,3)$ and $SC(2,4)$ obtained from ALICE data are
explained by the combinations
$\mathcal{K}_{22}+\frac{1}{2}\mathcal{K}_{04}-\mathcal{K}_{31}$ and
$\mathcal{K}_{22}+4\mathcal{K}_{11}^2$.
