  We show an analytic method to construct a bivariate distribution function
(DF) with given marginal distributions and correlation coefficient. We
introduce a convenient mathematical tool, called a copula, to connect two DFs
with any prescribed dependence structure. If the correlation of two variables
is weak (Pearson's correlation coefficient $|\rho| <1/3 $), the
Farlie-Gumbel-Morgenstern (FGM) copula provides an intuitive and natural way
for constructing such a bivariate DF. When the linear correlation is stronger,
the FGM copula cannot work anymore. In this case, we propose to use a Gaussian
copula, which connects two given marginals and directly related to the linear
correlation coefficient between two variables. Using the copulas, we
constructed the BLFs and discuss its statistical properties. Especially, we
focused on the FUV--FIR BLF, since these two luminosities are related to the
star formation (SF) activity. Though both the FUV and FIR are related to the SF
activity, the univariate LFs have a very different functional form: former is
well described by the Schechter function whilst the latter has a much more
extended power-law like luminous end. We constructed the FUV-FIR BLFs by the
FGM and Gaussian copulas with different strength of correlation, and examined
their statistical properties. Then, we discuss some further possible
applications of the BLF: the problem of a multiband flux-limited sample
selection, the construction of the SF rate (SFR) function, and the construction
of the stellar mass of galaxies ($M_*$)--specific SFR ($SFR/M_*$) relation. The
copulas turned out to be a very useful tool to investigate all these issues,
especially for including the complicated selection effects.
