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8 Volume LXV n. 1 – Gennaio-Marzo 2011 . (4) Being model (4) identical to model (2), except for the R parameter that has been added to the second component, it is clear that, by construction, it cannot perform worse; but how better can it do at the cost of one more parameter? As it can be seen from Table 1, for the Australian datasets the scores are almost always just below those of model (2). However, more substantial is the improvement in the fit of the Valencia Region dataset, with scores almost 30% lower. As it can be seen in Figure 2, model (4) outperforms model (2) in the accidental bump region, although it loses something by underestimating death at older ages. Figure 2 – Graduation of mortality data for the Valencia region (1999-2001) using model (4) (solid line) and model (2) (broken line). The observed qx values are indicated by dots. log(q x) -7 -6 -5 -4 -3 -2 -1 0 0 20 40 60 80 The last model we propose takes the component of (4) and the component of (3) x
Rivista Italiana di Economia Demografia e Statistica 9 . (5) Australian datasets graduated with (5) are still practically identical to those obtained with the other models. But it is for the Valencia Region dataset that this model leaves behind all others, scoring an that is 60% less than model (2). As it can be seen from Figure 3, model (5) fits better than model (2) both over the accidental bump and at older ages. Figure 3 – Graduation of mortality data for the Valencia Region (1999-2001) using model (5) (solid line) and model (2) (broken line). The observed qx values are indicated by dots. log(q x) -7 -6 -5 -4 -3 -2 -1 0 0 20 40 60 80 x
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SOCIETÀ E RIVISTA ADERENTI AL SIST
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