Studying electromagnetic waves in a magnetospheric plasma, it is often important to find their directions of propagation. When the assumption of a plane wave is not valid, the determination of the wave distribution function (WDF) is required. The WDF specifies the distribution of wave-energy density with respect to the frequency and the wave-normal direction. An alternative approach to the estimation of the experimentally accessible data for a given WDF is suggested with the hot-plasma and/or Doppler effects taken into account. The method is based on an explicit frequency dependence of the WDF. Examples of solutions, including the determination of the wave-refractive index, the wave-growth rate, the group velocity, and theoretical predictions of experimental data at predefined frequencies, are given in different cases. First, whistler-mode waves in a hot plasma near the geostationary orbit were studied. Second, the low-frequency waves observed by the low-altitude satellite Freja in the auroral zone were subjected to theoretical analysis. A complex, multimodal structure of the wave characteristics was found, mainly around the resonance angle. In the case of extremely short-wavelength waves, the influence of the Doppler effect produced qualitative changes of the wave-normal dependence of wave parameters. ¿ American Geophysical Union 1996