Monte Carlo simulation results. (a,b) Distribution of simulated bursts on the E_p − E_iso plane and the E_p − L_p plane for the on-axis cases. (c,d) Distribution of simulated bursts on the E_p − E_iso plane and the E_p − L_p plane for off-axis cases. The solid lines show the best-fitting results for the simulated data points, and the dashed lines represent the 3σ confidence level. To conclude, for on-axis bursts, the best-fit Amati relation is and the best-fit Yonetoku relation is . For off-axis bursts, the best-fit Amati relation is , while the best-fit Yonetoku relation is .