SalaryRank estimates ranks within reported salary bands using log-log interpolation. The graph below plots salary rank, S(x), against salary x, on a log-log  scale. For salaries above $100,000 the relationship is very close to linear, and for all salaries it is locally linear. Social Security Online reports data below $200,000 in narrow salary bands, only $5,000 wide. The buckets are broader above $200,000, but, as the graph shows, the relationship between log salary and log rank is very close to linear. In all cases, linear interpolation between log (x) and log (S(x)) can be expected to produce a good estimate.

The slope of the graph is consistent with a thick-tailed Pareto distribution of incomes, with shape parameter between 1.5 and 2.0. The curve predicts the highest (rank 1) salary is $1 to 2 billion, consistent with the estimated earnings of the most successful hedge fund managers.