*5.2. Fermi/GBM*

Prior to the removal of the 36 outlier bursts, MCLUST initially suggested a fit with four components in the *Fermi*/GBM sample. The fit included one group of bursts with very high or very low hardness ratios situated in a halo around the three groups in Figure 5b. These outlier bursts were effectively removed using HDOutliers (Section 2), following previous studies including Tóth et al. [46], Horváth et al. [56,58] and were likely the result of unsuitable background subtraction. Upon removal of the outliers, MCLUST identified three components, which were similar to the components obtained for *Swift*/BAT (Figure 5b). The intermediate duration component contained more bursts than the class identified by Horváth et al. [56], whose intermediate class only contained bursts with low spectral hardness. This difference can be attributed to their smaller sample size of 1298 bursts.

A signature of a Gaussian component is visible at the sharp boundary between the intermediate and long duration components in Figure 5b, indicating an arbitrary Gaussian component was identified. Consistent with the results obtained for *Swift*/BAT, the intermediate component was disregarded when clustCombi was applied, indicating that it was likely an overfitting component identified by the GMM clustering procedure. Thus, a short and long duration class remained.

In this analysis, the hardness ratio was computed using the background-subtracted counts to be consistent with previous *Fermi*/GBM studies and to enable direct comparison with those results. The short and long duration classes in Figure 6 were comparable to the classes found in previous GMM clustering analyses by Bhave et al. [54], Bhat et al. [87], and in skewed bi-variate fits carried out by Tarnopolski [51]. Table 4 and Figure 7 show

that the short duration class was spectrally harder than the long duration class, as expected. The mean duration of the classes were 0.64 s (1 *σ* standard deviation of 0.65 s) and 38.6 s (1 *σ* standard deviation of 23.4 s) for the short and long classes, respectively. This result is consistent with the mean durations of the short (0.82 s) and long (28.3 s) classes identified in the GMM clustering of the third *Fermi*/GBM catalogue [87].
