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Far-ultraviolet (FUV) and far-infrared (FIR) luminosity functions (LFs) ofgalaxies show a strong evolution from $z = 0$ to $z = 1$, but the FIR LFevolves much stronger than the FUV one. The FUV is dominantly radiated fromnewly formed short-lived OB stars, while the FIR is emitted by dust grainsheated by the FUV radiation field. It is known that dust is always associatedwith star formation activity. Thus, both FUV and FIR are tightly related to thestar formation in galaxies, but in a very complicated manner. In order todisentangle the relation between FUV and FIR emissions, we estimate the UV-IRbivariate LF (BLF) of galaxies with {\sl GALEX} and {\sl AKARI} All-Sky Surveydatasets. Recently we invented a new mathematical method to construct the BLFwith given marginals and prescribed correlation coefficient. This method makesuse of a tool from mathematical statistics, so called "copula". The copulaenables us to construct a bivariate distribution function from given marginaldistributions with prescribed correlation and/or dependence structure. Withthis new formulation and FUV and FIR univariate LFs, we analyze various FUV andFIR data with {\sl GALEX}, {\sl Spitzer}, and {\sl AKARI} to estimate the UV-IRBLF. The obtained BLFs naturally explain the nonlinear complicated relationbetween FUV and FIR emission from star-forming galaxies. Though the faint-endof the BLF was not well constrained for high-$z$ samples, the estimated linearcorrelation coefficient $\rho$ was found to be very high, and is remarkablystable with redshifts (from 0.95 at $z = 0$ to 0.85 at $z = 1.0$). This impliesthe evolution of the UV-IR BLF is mainly due to the different evolution of theunivariate LFs, and may not be controlled by the dependence structure.

Far-Ultraviolet and Far-Infrared Bivariate Luminosity Function of Galaxies: Complex Relation between Stellar and Dust Emission