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Fig. 3. Parametric shape index P_BC according to Eq. [7] and P_vG according to Eq. [9a], [10a], and [8], that is, the first- and second-order approximation and the exact expression, computed from optimized ${theta}$ _r, ${theta}$ _s, ${lambda}$ , m, and n as a function of the experimental shape index, P, using samples from UNSODA with a positive ${theta}$ _r. Coefficients for the correlation between all shape indices are provided in the insert.