  We study the relationship between the K-band and the sub-millimetre (submm)
emissions of nearby galaxies by computing the bivariate K-band-submm luminosity
function (BLF) of the Herschel Reference Survey (HRS), a volume-limited sample
observed in submm with Hersche/SPIRE. We derive the BLF from the K-band and
submm cumulative distributions using a copula method. Using the BLF allows us
to derive the relationship between the luminosities on more solid statistical
ground. The analysis shows that over the whole HRS sample, no statistically
meaningful conclusion can be derived for any relationship between the K-band
and the submm luminosity. However, a very tight relationship between these
luminosities is highlighted, by restricting our analysis to late-type galaxies.
The luminosity function of late-type galaxies computed in the K-band and in the
submm are dependent and the dependence is caused by the link, between the
stellar mass and the cold dust mass, which has been already observed
