Replication package for 'The Optimal Mean: A Monotone Arithmetic-Geometric Gap Correction Weighted by the Herfindahl-Hirschman Index'

Code, data and generated outputs reproducing every table and figure of the paper 'The Optimal Mean: A Monotone Arithmetic-Geometric Gap Correction Weighted by the Herfindahl-Hirschman Index'. The proposed rule is M_*(x) = M_a(x) - [1 - HH(x)]/2 * [M_a(x) - M_g(x)] = [(1+HH)/2] M_a + [(1-HH)/2] M_g, where M_a and M_g are the arithmetic and geometric means and HH is the Herfindahl-Hirschman index of the normalized component shares. The package contains the replication backend (Monte Carlo diagnostics, monotonicity stress tests, figure data), the HDI 2023 and WGI 2022 real-data applications, the WGI measurement-error propagation (Section 7.2), and the comparison with unbalance-penalty indices (AMPI; penalized geometric and power means, Section 7.3). All stochastic runs use fixed seed 20260701.