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.
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