  Statistical studies of gamma-ray burst (GRB) spectra may result in important
information on the physics of GRBs. The Fermi GBM catalog contains GRB
parameters (peak energy, spectral indices, intensity) estimated fitting the
gamma-ray SED of the total emission (fluence, flnc), and during the time of the
peak flux pflx. Using contingency tables we studied the relationship of the
models best fitting pflx and flnc time intervals. Our analysis revealed an
ordering of the spectra into a power law - Comptonized - smoothly broken power
law - Band series. This result was further supported by a correspondence
analysis (CA) of the pflx and flnc spectra categorical variables. We performed
a linear discriminant analysis (LDA) to find a relationship between categorical
(spectral) and model independent physical data. LDA resulted in highly
significant physical differences among the spectral types, that is more
pronounced in the case of the pflx spectra, than for the flnc spectra. We
interpreted this difference as caused by the temporal variation of the spectrum
during the outburst. This spectral variability is confirmed by the differences
in the low energy spectral index and peak energy, between the pflx and flnc
spectra. We found that the synchrotron radiation is significant in GBM spectra.
The mean low energy spectral index is close to the canonical value of {\alpha}
= -2/3 during the peak flux. However, $\alpha$ is ~ -0.9 for the spectra of the
fluences. We interpret this difference as showing that the effect of cooling is
important only for the fluence spectra.
