  More than 50% of Active Galactic Nuclei (AGNs) are suspected to be red and
affected by dust-obscuration. Meanwhile, popular spectral diagnostics of AGNs
are based on optical or ultraviolet light, making the dust obscuration as a
primary concern for understanding the general nature of AGNs and supermassive
black holes residing in them. To provide with a method of investigating
properties of the dusty AGNs, we derive new black hole (BH) mass estimators
based on velocity widths and luminosities of Near Infrared (NIR) hydrogen
emission lines such as P$\alpha$ and P$\beta$, and also investigate the line
ratios of these Hydrogen lines. To derive the BH mass ($M_{\rm BH}$)
estimators, we used a sample of 37 unobscured Type-1 AGNs with a $M_{\rm BH}$
range of $10^{6.8}$-$10^{9.4} M_{\odot}$, where $M_{\rm BH}$ come from either
reverberation mapping method or single-epoch measurement method using Balmer
lines. Our work shows that $M_{\rm BH}$ can be estimated from the Paschen line
luminosities and the velocity widths to the accuracy of 0.18 - 0.24 dex (rms
scatter). We also show that the mean line ratios of the Paschen lines and the
Balmer lines are $\mathrm{\frac{H\alpha}{P\alpha}} \simeq 9.00$,
$\mathrm{\frac{H\beta}{P\alpha}} \simeq 2.70$, which are consistent with a Case
B recombination under a typical AGN broad line region environment. These ratios
can be used as reference points when estimating the amount of dust extinction
over the broad line region (BLR) for red AGNs. We expect the future application
of the new BH mass estimators on red, dusty AGNs to provide a fresh view of
obscured AGNs.
