Eccentricity distributions for (a) GTPs, (b) all transiting BDs (P > 10 d), (c) LMS companions, and (d) the BD subsample with P > 16 d. Step histograms use uniform bins in e; solid curves show the single-Beta maximum-likelihood fit to each panel (annotated by (α, β)). Sample sizes are indicated in the legends. BDs (P > 16 d) resemble LMSs more than GTPs, with a higher, more concentrated mid-e preference, whereas the all-BDs distribution is pulled toward the GTP-like shape by the short-period, low-e objects. This visual comparison complements our statistical results (ES permutation p = 0.016 for GTP vs. BD(> 16 d); non-separation of BD(> 16 d) from LMS at current N).