Anharmonic vibrational numbers and densities of states are calculated by quantum-corrected Monte Carlo integration of phase space volumes on ab initio potential energy surfaces for HO2, H2CO, and H2O2. Rotational dependences of the anharmonicity are also determined for H2CO. The total numbers of states W(E, J = 0) are approximated in analytical form. Using Whitten-Rabinovitch expressions as a reference, anharmonicity factors F-anh,F-rho(E,J = 0) for the densities of states are also given analytically. The results are used as a benchmark for comparisons with an empirical anharmonicity model (Troe, J. Chem. Phys. 1995, 190, 381). It was found that some modifications of this model are necessary for applications at high energies. The improved empirical model is intended to serve for estimates of anharmonic densities of states of larger molecular systems at high energies.