Parameters
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We mainly focus on line parameters of broad H$\alpha$ of 3C390.3, due to the following two main reasons. On the one hand, the broad H$\alpha$ is much stronger than the broad H$\beta$, which leads to more reliable line parameters. On the other hand, there is much less contamination on the broad H$\alpha$. Only the narrow emission lines, the narrow H$\alpha$ and \[N [ii]{}\] doublet, have effects on the measured line parameters of the double-peaked broad H$\alpha$. However, for the double-peaked broad H$\beta$, besides the common narrow H$\beta$ and \[O [iii]{}\] doublet, the extended \[O [iii]{}\] doublet and some weak optical Fe [ii]{} emission lines (Dietrich et al. 2012) have effects on the measured line parameters of the broad H$\beta$. Thus, focusing on the observed spectrum around H$\alpha$ of 3C390.3 should lead to more accurate line parameters and to find more reliable correlation of the line parameters.

For 3C390.3, there are 67 public spectra observed around 1995 including available H$\alpha$ which can be collected from the AGNWATCH project, based on those reported parameters listed in Table 9 in Dietrich et al. (1998). Then the line parameters of the double-peaked broad H$\alpha$ are measured as follows. In order to ignore 