Statistical Properties of the GRBM Catalog of GRBs

The $T_{90}$ duration distribution is consistent with the BATSE bimodal duration distribution; in particular, the GRBM catalog turns out to include fewer short duration ($T_{90}<2$ s) bursts than BATSE, as expected on the basis of the on-board trigger logic parameters selected: these parameters lower the GRBM sensitivity to short bursts. Also the correlation between spectral hardness and duration discovered by BATSE is confirmed within the GRBM catalog: on average, short bursts are significantly harder. In particular, the hardness ratios, computed as the ratio of the $>$ 100 keV counts over the 40-700 keV counts, are distributed normally around the value $0.72$ and $\sigma = 0.12$. This property definitely supports the hardness ratio threshold condition $>0.3$, i.e. $3.5\sigma$ lower than the mean value. Concerning the peak count rate and total counts cumulative distributions, these confirm fewer dim bursts than expected for a homogeneous distribution within an Euclidean space.