These show the posterior distributions as supplementary material for arXiv:2305.18293 and doi:10.1093/mnras/stae1219 The corner plots for the complete 20 parameters with amplitudes hc = 0.5e-15, 1e-15, 2e-15, 3e-15, and 4e-15 for both circular and eccentric population of SMBHBs are presented in the 'free_parameters' folder. The corner plots for the 16 parameters with amplitudes hc = 0.5e-15, 2e-15, and 4e-15 for both circular and eccentric population of SMBHBs using the fitted BH-bulge mass parameters from the simulations can be found in the 'simulation_parameters' folder. The posterior distributions are shown as black contours, while the prior distributions are denoted by light green lines. The top right inlay figure shows the median and central 2sigma range of the recovered characteristic spectrum, where the 5 points denote the frequency bins of 1/(25years), 2/(25years), 3/(25years), 4/(25years) and 5/(25years), which are used as the input data for the Bayesian analysis. To guide the eye the analytic sensitivity curve from the IPTA DR2 is also plotted.