p-values from the K − S tests as a function of the index α from Eq. (1). The solid lines show the results for each class of sampled neutrino blazar candidates. The error bars show the standard deviation of each p-value after repeating the test 10³ times for each α. The dashed lines show the results for the test performed on the control samples with shaded areas indicating the 1σ uncertainty regions from the N = 1000 Monte Carlo samples drawn for each α and source class. The upper panel shows the results from T1 (gamma-ray energy flux as proxy for the luminosity), while the lower panel shows the results from T2 (using only sources with known redshift).