The effect of the spectral index range on the limit result. Left: lower limits at 95% confidence level as a function of spectral index range. The lower and upper bounds of the range can vary between 0 ≤ α_min ≤ 1 and 0 ≤ α_max ≤ 4, respectively. Values above the red line satisfy the criterion of convergence of the cumulative distribution (see right panel). We adopted a lower limit, α > 2.2, obtained using the α_min = 0 ≤ α ≤ 4 = α_max range. Right: convergence of the cumulative probability function with varying spectral index ranges. Values above the red line have ϵ < 1%, which we used as an acceptance criterion (see Eq. (5)).