Differential parameter distributions for critical LAH physical characteristics. The panels show distributions for σ (blue), r_sH (red), and f_H (black), with the top row showing a histogram of input sample LAHs, and the bottom panel the binned 1/V_max distributions. Individual bins are shown as diamonds with error bars, with the best functional fit shown by the solid or dot-dash lines. Solid lines are lognormal fits, used for the σ and f_H distributions, while the r_sH distribution was best fit by a broken power law (dot-dash line). The shaded region shows the inter-quartile range of possible fit parameters. The best-fit values are given in Table 2.