The Lyman edge region (912 angstrom) of quasars is thought to be formed by thermally emitting accretion disks and would be affected by broad-line region (BLR) clouds. The Lyman edge discontinuities in disk models are predicted both in absorption (less-than-or-equal-to 80%) and in emission (less-than-or-equal-to 30%). For BLR clouds, the predictions range from complete absorption at the Lyman edge for large BLR clouds to ubiquitous (approximately 10%) absorption edges for an isotropic mist of clouds. The IUE archives provide a number of objects to search for the features predicted by these different models. By optimally extracting spectra and co-adding multiple spectra, a systematic search for discontinuities as small as 15% is possible in the typical S/N spectra. In our sample of 49 quasars, 38% of the AGNs do not show any discontinuity at any redshift. Discontinuities at redshifts smaller than the AGN emission redshift are seen in 28% of the sample. These discontinuities are associated with intervening gas extrinsic to the AGN environment. Discontinuities at the AGN emission redshift potentially due to associated gas in the AGN environment are seen in 22% of the sample. However, only 10% of the sample shows discontinuities at the emission redshift which cannot be associated with any known absorption-line systems. Our analysis indicates that only those accretion disk models in which most of the AGNs show Lyman edge discontinuities of less-than-or-equal-to 15% are consistent with the observations. If the Lyman edge discontinuity is due to large BLR clouds, the observations indicate that the gas column densities are less than almost-equal-to 10(22) cm-2.