Summary statistics, P(ρ) (top left), W₁ (bottom left), and χ (bottom right), for a set of N_real = 100 realisations of a highly non-Gaussian field with ξ₀ = 27 and other parameters of Δ = 0.25, R = 1, L = 4000 × Δ, α = 3/2, and N_pts = 40 × 2000². The difference between P(ρ) and the MF prediction is also presented (top right). Error bars show the standard deviation, and the points the sample means. The BMF estimates of the PDF (solid blue lines, top panels) and W₁ (bottom left panel) remain an excellent approximation for ξ₀ > 20. The MF limit is a good approximation for all statistics in the high-density tails.