*4.2. Fermi/GBM*

BIC

For *Fermi*/GBM, the initial MCLUST fit indicated that a three-component fit to the data was preferred. The BIC values of the top three models are shown in Figure 5a. The three best-fit components are depicted in Figure 5b. The three-component 'VEI' model exhibited a BIC value difference of ∼6 compared to the next best model; thus, it was considered a significant result. The classification components were labelled 'short', 'intermediate', and 'long', according to their duration. The boundary between the 'intermediate' and 'long' components exhibited a similar round-edge feature as identified in the results for *Swift*/BAT.

(**b**) **Figure 5.** (**a**) BIC values of the top three MCLUST models fit to the *Fermi*/GBM sample and (**b**) the resulting duration-hardness plane for the best-fit three-component model (VEI).

The results obtained from applying clustCombi to this sample are shown in Figure 6, indicating that a model consisting of two components or classes, rather than three, provided a better fit to the data, based on a decrease in entropy depicted in the entropy plot in Figure 2. The number of bursts in the 'long' and 'short' classes identified by clustCombi is presented in Table 2.

**Figure 6.** The results of clustCombi applied to the components identified by MCLUST in the durationhardness plane for *Fermi*/GBM.

The violin plot in Figure 7 for the *Fermi*/GBM sample demonstrates the distributions of the duration and hardness ratio, while the summary statistics of these populations are presented in Table 4.

**Figure 7.** Violin plots showing the distribution of the duration (T90) and hardness ratio (HR32) for the *Fermi*/GBM 'short' (red) and 'long' (blue) classes identified by clustCombi. The median of each parameter is marked as a black line within the box, which represents the 1 *σ* interval (i.e., the 16th to 84th percentile).


**Table 4.** Mean (*µ*), standard deviation (*σ*), and median of the properties of the *Fermi*/GBM 'long' and 'short' classes identified by clustCombi.
