  Spectra in astroparticle physics are commonly approximated by simple power
laws. The steeply falling nature of these power laws, however, makes the
detection of additional components rather challenging. This holds true
especially, if the additional components are small compared to the established
ones. Energy spectra of muon neutrinos are an interesting example of such a
scenario, where the conventional and astrophysical components to the spectra
have been established by the use of different analysis methods, such as
likelihood fits or spectral deconvolution. The prompt component, although
expected from theoretical models, has not yet been experimentally observed.
Furthermore, the extraction of physics parameters is challenged by the large
systematic uncertainties, especially at high energies. This contribution
presents a different approach to the analysis of power-law spectra, which is
based on functional data analysis. The method itself and its implications are
discussed using muon and neutrino energy spectra as an example.
