We present the ab initio calculations of the on-site hybridization between Ce 4f and Ce 5d electrons as well as the Mulliken Ce 5d occupation for the doped Kondo insulators CeRhSb and CeNiSn. In our investigations we have examined the following series: CeRhSb1 − xSnx, CeRh1 − xPdxSb, CeRhSb1 − xTex, Ce1 − xLaxRhSb and CeNi1 − xCuxSn, CeNiSn1 − xSbxSb, Ce1 − xLaxNiSn. The transition from the Kondo insulator to the metallic state induced by doping at some critical concentration xc was recently reported for various dopants based on the resistivity, susceptibility and spectroscopic data. Our calculations show that both the Mulliken occupation of Ce 5d states and the onsite hybridization between Ce 4f and Ce 5d states exhibit critical behavior at nearly the same dopant concentrations as observed in experiment. We also note that for the CeRhSb-based alloys the disorder is not necessary to explain their critical behavior, in contrast to the CeNiSn-based series.