Three model electron distribution functions representative of the region between the plasmapause and the geostationary orbit are constructed. These models are used to compare numerical solutions of the hot electromagnetic dispersion equation with analytical solutions of the quasielectrostatic dispersion equation, and to compare numerical and analytical solutions of the electrostatic dispersion equation, for whistler mode propagation at wave normal angles θ close to the resonance cone angle θR. It is shown that the quasielectrostatic solutions are a reasonable approximation for all three models when θ θR the approximation only remains good inside the plasmapause for frequencies ω equal to 0.4 times the electron gyrofrequency Ω. For θ > θR the agreement between numerical electromagnetic and electrostatic solutions is good whenωΩ⩽ 0.6. Numerical results show that forωΩ= 0.8the solutions to the quasielectrostatic equation for large refractive index correspond to strongly damped waves for each model.