recent papers that attempt to correct  mass determinations to better agree with those based on other lines [e.g., @Runnoe13; @Coatman17; @Mejia18; @Marziani19].

Characterizing Line Widths
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It is our suspicion that the apparent difficulties with -based masses trace back not only to the $S/N$ issue, but also to how the line widths are characterized. It has been customary in AGN studies to characterize line widths by one of two parameters, either FWHM or the line dispersion , which is defined by $${\mbox{$\sigma_{\rm line}$}}= \left[ \frac{ \int (\lambda - \lambda_0)^2 P(\lambda)\,d\lambda}{\int P(\lambda)\,d\lambda} \right]^{1/2},
\label{eq:Defsigl}$$ where $P(\lambda)$ is the emission-line profile as a function of wavelength and $\lambda_0$ is the line centroid, $$\lambda_0 = \frac{\int \lambda P(\lambda)\,d\lambda}{\int P(\lambda)\,d\lambda}.
\label{eq:Deflambda0}$$ While both FWHM and  have been used in the virial equation to estimate AGN black hole masses, they are not interchangeable. It is well known that AGN line profiles depend on the line width [@Joly85]: broader lines have lower kurtosis, i.e., they are “boxier” rather than “peakier.” Indeed, for AGNs, the ratio ${\rm FWHM}/{\mbox{$\sigma_{\rm line}$}}$ has been found to be a simple but useful characterization of the line profile [@Collin06; @Kollatschny13].

Each line-width measure has practical strengths and weaknesses [@Peterson04; @Wang20]. The line 