We compare data from the Diffuse InfraRed Background Experiment (DIRBE) on the Cosmic Background Explorer (COBE) satellite to the the Wainscoat et al. (1992) model of the infrared sky. The model is first compared with broadband K (2.2 microns) star counts. Its success at K gives credence to its physical approach which is extrapolated to the L band (3.5 microns). We have analyzed the histograms of the pixel by pixel intensities in the 2.2 and 3.5 micron maps from DIRBE after subtracting the zodiacal light. The shape of these histograms agrees quite well with the histogram shape predicted using the Wainscoat et al. model of the infrared sky, but the predicted histograms must be displaced by a constant intensity in order to match the data. This shift is the cosmic infrared background, which is 16.9+/-4.4 kJy/sr or 23.1+/-5.9 nW/m^2/sr at 2.2 microns, and 14.4+/-3.7 kJy/sr or 12.4+/-3.2 nW/m^2/sr at 3.5 microns.
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