can be estimated by (Peterson et al. 2004) $$\begin{split}
&\sigma_{H\alpha}^2  = \frac{\int_{\lambda}\lambda^2\times 
P_{\lambda}d\lambda}{\int_{\lambda}P_{\lambda}d\lambda} - 
(\frac{\int_{\lambda}\lambda\times P_{\lambda}d\lambda}
{\int_{\lambda}P_{\lambda}d\lambda})^2 \\
&flux(H\alpha) = \int_{\lambda}P_{\lambda}d\lambda
\end{split}$$ where $P_{\lambda}$ is the line profile of the double-peaked broad H$\alpha$ after subtraction of the narrow lines. Here, the main reasons to use the second moment rather than FWHM (full width at half maximum) are: the second moment rather than the FWHM can be used to well trace kepler velocities of broad line clouds in BLR of AGN (Fromerth & Melia 2000, Peterson et al. 2004), the second moment rather than the FWHM is well defined for arbitrary line profiles (such as the double-peaked broad line profile), and moreover the second moment rather than the FWHM has relatively lower uncertainty (Peterson et al. 2004). The measured line widths ($\sigma$) of the double-peaked broad H$\alpha$ from the observed spectra are listed in Table 1.

Before proceeding further, it is necessary to estimate the corresponding uncertainty of the measured line width of the double-peaked broad H$\alpha$. Here, the commonly used bootstrap method (Peterson et al. 1998, 2004, Press et al. 1992, Zhang 2011b) is applied to estimate the uncertainty. Based on each observed double-peaked broad H$\alpha$ with narrow lines (\[N 