Spatial analysis of tails of air pollution PDFs in Europe

The paper states that heavy-tailed air-pollution PDFs are well fit by q-exponentials (its Eq. (1)) and motivates this via superstatistics, asserting q = ⟨λ̂²⟩/⟨λ̂⟩² (its Eq. (2)), with T determined by the local-window kurtosis Kexp = 9 (its Eq. (3)) . The candidate solution derives, in detail, that a normalized exponential snapshot mixed with a Gamma prior yields an exact Lomax/Pareto-II law that equals the q-exponential with q = (α+2)/(α+1), and explains that this corresponds to using the λ-tilted prior for the mixing (Type-B), rather than the bare prior implicit in Eq. (2) (Type-A). Both are standard in superstatistics and differ by whether one mixes unnormalized Boltzmann factors (∼e^{-λx}) or normalized exponentials (λe^{-λx}). The kurtosis-9 criterion and the scaling E[X] ∝ λ^{-1} are correctly used by the paper and are rigorously justified by the model; the paper’s statement on E[X] being proportional to λ^{-1} is conceptually correct but silently assumes q < 3/2 for finiteness of the mean . Overall: same phenomenon, different (Type-A vs Type-B) derivations, plus minor missing assumptions in the paper.