Distributions of the ERS and energy flux of MXFs. (a) Probability distribution of the phenomenological ERS proxy. Black points show S_γ evaluated at γ = 0.94, and the solid red curve shows the best-fitting right-Pareto lognormal (rPln) model. (b) Probability distribution of the energy flux. Gray points with error bars show the observed distribution, and the red solid curve shows the best-fitting thresholded power-law (TPL) model. The vertical dotted line marks the threshold flux F₀ = 7.9 × 10⁻⁷ erg cm⁻² s⁻¹. The best-fitting high-flux slope is α_F = 2.23 ± 0.10.