Figure 5

Curve of α ( e ) Obtained from the Gaussian Mixture Model from Real Data The curve of α(e) is monotone decreasing in the area of [-4, 0.5], which agree with the existing knowledge. However, the curve unexpectedly ramps up (the broken line)due to the heavier tail of the positive component. To resolve this problem, we simply fix the curve to be a constant. This heuristic is simple but works well in practice. The solid line in Figure 4 visualizes α(e) with this heuristic