the PDFs of Eps,(4.2)and (4.4) are plotted in Fig. 1, while the HRFs are plotted in Fig. 2. It can be noticed from these two figures that the PDFs are all descreasing functions with mode at 0, while the HRFs are increasing-constant functions.
Based on Eq. (4.4), the Bayesian prediction bounds for Y are given by (3.11)