*4.1. Swift/BAT*

The BIC values for the top three models versus the number of components, resulting from the application of MCLUST to the full *Swift*/BAT sample, are shown in Figure 1a. The 'VEI' model with three components had the largest BIC value. The three components were labelled 'long', 'intermediate', and 'short' according to their durations and are projected onto the hardness-duration plane in Figure 1b. The clear round edge between the intermediate and long components suggests that a Gaussian was being fit to a non-Gaussian component.

**Figure 1.** *Cont.*

BIC

(**b**) **Figure 1.** (**a**) BIC values of the top three MCLUST models fit to the *Swift*/BAT sample and (**b**) the resulting duration-hardness plane for the best-fit three-component model (VEI).

After clustCombi was applied, the 'intermediate' and 'long' components were combined, producing a large decrease in entropy as shown in Figure 2. The two remaining components or classes were labelled 'long' and 'short', as shown in Figure 3. Table 2 presents the sample size of the classes.

**Figure 2.** Entropy plots returned by clustCombi depicting the entropy of the initial MCLUST fits (three components) and the entropy after combination of the initial MCLUST components for *Swift*/BAT (left) and *Fermi*/GBM (right). An inflection, or elbow, in the entropy plot signifies a model with the optimal number of components.

**Figure 3.** The results of clustCombi applied to the components identified by MCLUST in the durationhardness plane for *Swift*/BAT.

The distributions of the duration (T90) and hardness ratio (HR32) are depicted in the violin plot in Figure 4. The mean, standard deviation, and median values of these parameters for the long and the short classes are presented in Table 3.

**Figure 4.** Violin plots showing the distribution of the duration (T90) and hardness ratio (HR32) for the *Swift*/BAT '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 3.** Mean (*µ*), standard deviation (*σ*), and median of the properties of the *Swift*/BAT 'long' and 'short' classes identified by clustCombi.

