Databases of the absorption line blackbody distribution function (ALBDF) of CO2 and H2O were generated over a wide range of gas and blackbody temperatures and the full range of gas concentration from line-by-line (LBL) calculations using the latest version of HITEMP. Proper orthogonal decomposition (POD) and the hyperbolic correlations (HC) were then used for rapid calculation the ALBDF value at an arbitrary combination of gas and blackbody temperatures and gas concentration. A novel hyperbolic correlation for H2O was proposed to fully account for the self-broadening effect. The accuracy of POD and the HC was evaluated by comparing the ALBDF values and the total gas emissivities from these two approximate methods at several selected conditions against those from LBL calculations. POD is significantly more accurate than HC at essentially no extra computational costs.