  We have revisited the spectral width in the EF E spectrum of gamma-ray bursts
with the BEST peak flux P and time-integrated F spectral data provided by the
Fermi GBM Burst Catalog. We first compute the BEST spectral widths to compare
with some typical physics models. Our analysis results consist with the
previous results: blackbody emission alone cannot explain the observed spectrum
and most of the observed spectra cannot be interpreted by the synchrotron
radiation. We then check the correlations between the spectral width and the
observable model-independent burst properties of duration, fluence, and peak
flux and find that positive correlations exist between them for both the P and
F spectra. Moreover, the short burst appears to extend the correlation found
for the long burst. We further demonstrate that these positive correlations
also exist in the cosmological rest frame; that is, the spectral width
correlates with the isotropic-equivalent energy E iso as well as the
isotropic-equivalent peak luminosity L iso for different energy bands and
timescales. Our results show that the wider bursts have larger energy and
luminosity. Moreover, short bursts would appear to extend this trend
qualitatively. Taking the Amati relation into account, we tend to believe that
the spectral shape is related to energy and luminosity.
