  We present a new optical luminosity-HI mass bivariate luminosity function
(BLF) based on HI line observations from the Nancay Interstellar Baryons Legacy
Extragalactic Survey (NIBLES). NIBLES sources lie within the local universe
(900 $\leq cz \leq$ 12,000 \kms) and were chosen from SDSS DR5 such that the
optical luminosity function was sampled as uniformly as possible. The HI mass
function (HIMF) derived from our raw-data BLF, which is based on HI detections
only, is consistent with the HIMFs derived from other optically selected
surveys in that the low-mass slope is flatter than those derived from blind HI
surveys. However, spanning the entire luminosity range of NIBLES, we identify a
highly consistent distribution of the HI gas mass to luminosity ratio
(gas-to-light ratio) with a predictable progression in the mean MHI/Lr ratio as
a function of Lr. This consistency allows us to construct plausible
gas-to-light ratio distributions for very low-luminosity bins which lie outside
the NIBLES sample. We also identify a $\sim$ 10% decrease in detection fraction
for galaxies fainter than log(\Lr) = 9.25, consistent with the expected
decrease due to distance and sensitivity effects. Accounting for these trends,
we reconstruct plausible gas-to-light distributions spanning luminosity bins
down to log(\Lr) = 5.25, thus producing a corrected BLF. This corrected BLF is
in good qualitative agreement with optical luminosity-HI mass distributions
from the ALFALFA survey and is able to accurately reproduce blind survey HIMFs,
lending credibility that this two dimensional optical luminosity-HI mass
distribution is an accurate representation of the volume density distribution
of galaxies in the local universe. We also note that our agreement with HIMFs
from other surveys is dependent on accounting for all systematic differences
such as selection method, Hubble constant and HI flux scale.
