  We discuss the results of the relationships between the K-band and stellar
mass, far-infrared luminosities, star formation rate, dust and gas masses of
nearby galaxies computing the bivariate K-band Luminosity Function (BLF) and
bivariate K-band Mass Function (BMF) of the Herschel Reference Survey (HRS), a
volume-limited sample with full wavelength coverage. We derive the BLFs and
BMFs from the K-band and stellar mass, far-infrared luminosities, star
formation rate, dust and gas masses cumulative distributions using a copula
method which is outlined in detail. The use of the bivariate computed taking
into account the upper limits allows us to derive on a more solid statistical
ground the relationship between the observed physical quantities. The analysis
shows that the behaviour of the morphological (optically selected) subsamples
is quite different. A statistically meaningful result can be obtained over the
whole HRS sample only from the relationship between the K-band and the stellar
mass, while for the remaining physical quantities (dust and gas masses, far-IR
luminosity and star formation rate), the analysis is distinct for late-type
(LT) and early-type galaxies (ETG). However, the number of ETGs is small to
perform a robust statistical analysis, and in most of the case results are
discussed only for the LTG subsample. The Luminosity and Mass Functions (LFs,
MFs) of LTGs are generally dependent on the K-band and the various dependencies
are discussed in detail. We are able to derive the corresponding LFs and MFs
and compare them with those computed with other samples. Our statistical
analysis allows us to characterise the HRS, that, although non homogeneously
selected and partially biased towards low IR luminosities, may be considered as
representative of the local LT galaxy population.
