Distribution of log-parabola parameters (from Eq. (2)) for 100 000 sources simulated with a model consisting of a log-parabola, an elliptical galaxy host, and a dust torus (grey histogram). We see that, overall, the sources within the blazar locus (blue histogram) present weak spectral curvature (β < 0.04 for 50% of the sample) and concentrate around E_p ≈ 1.5 × 10⁻¹³ erg. The black hatched histograms represent the blazar locus after we apply the WISE magnitude cuts and can be divided into two components, one with FSRQs (red histograms), and the other with BL Lacs (green histograms).