Power analysis for non-step potentials. (A) Black line: state density q(d) for M = 100 circular objects Y with radius R = 3.57 randomly placed in a square domain of size 200 × 200; R is chosen to yield a circle-covered area fraction of 0.1; Colored lines: resulting distance distribution p(d) for the three potentials shown in B. (B) Plummer potential (Eq. 12) with ϵ = 1 and varying scale parameter. (C) Monte-Carlo estimates of 80%-power isolines in the N-a-plane; dashed lines: tests based on Tst, solid lines: tests based on Tpl. Note that larger kinks in the dashed lines are due to the discreteness of Tst and are statistically significant. Colors in A-C indicate scale parameters of the true potential; red: σ = 0.2, green: σ = 1.0, and blue: σ = 5.0.