rivista italiana di economia demografia e statistica - Sieds

10
Volume LXV n. 1 – Gennaio-Marzo 2011
Table 1 – Graduation parameters for the male and female Australian national mortality
data for the periods 1946-48, 1960-62 and 1970-72 (Heligman and Pollard,1980) and for
the Valencia Region, merged gender, mortality dataset for the period 1999–2001, (Debòn
et al., 2005, 2006).
Dataset Model A B C D E F G H K R
Austr. F. 1946-48 (2) 0,451 0,003 0,077 0,171 0,001 3,44 31,658 0,00021 1,015 1,371
Austr. F. 1960-62 (2) 0,457 0,002 0,071 0,166 0,000 22,59 19,173 0,00013 1,022 1,303
Austr. F. 1970-72 (2) 0,508 0,001 0,049 0,148 0,000 24,07 18,255 0,00009 1,037 1,196
Austr.M. 1946-48 (2) 0,287 0,003 0,015 0,117 0,001 7,47 20,703 0,00002 1,326 0,787
Austr.M. 1960-62 (2) 0,371 0,002 0,007 0,103 0,001 10,68 20,800 0,00002 1,319 0,795
Austr.M. 1970-72 (2) 0,441 0,002 0,007 0,100 0,002 15,19 20,134 0,00001 1,352 0,782
Austr. F. 1946-48 (3) 0,457 0,003 0,034 0,134 0,001 1,76 38,210 49,590400 143,140 0,099
Austr. F. 1960-62 (3) 0,552 0,002 0,033 0,133 0,000 11,81 19,857 124,964000 158,045 0,095
Austr. F. 1970-72 (3) 0,509 0,001 0,029 0,128 0,000 18,72 18,448 110,80100 157,730 0,094
Austr.M. 1946-48 (3) 0,301 0,003 0,020 0,125 0,001 8,67 20,415 0,55960 93,350 0,096
Austr.M. 1960-62 (3) 0,356 0,002 0,011 0,113 0,001 11,82 20,663 0,44089 90,135 0,099
Austr.M. 1970-72 (3) 0,414 0,002 0,010 0,110 0,002 16,33 20,058 0,40693 88,119 0,103
Austr. F. 1946-48 (4) 0,413 0,003 0,089 0,180 0,001 4,77 36,320 0,00027 1,010 1,464 1,926
Austr. F. 1960-62 (4) 0,417 0,002 0,073 0,168 0,000 5087,68 18,978 0,00013 1,021 1,313 2,889
Austr. F. 1970-72 (4) 0,505 0,001 0,049 0,149 0,000 18,88 18,242 0,00009 1,037 1,195 0,900
Austr.M. 1946-48 (4) 0,287 0,003 0,015 0,117 0,001 7,94 20,710 0,00002 1,326 0,787 1,035
Austr.M. 1960-62 (4) 0,370 0,002 0,007 0,104 0,001 9,36 20,765 0,00002 1,321 0,793 0,928
Austr.M. 1970-72 (4) 0,439 0,002 0,007 0,101 0,002 13,27 20,132 0,00001 1,366 0,776 0,936
Austr. F. 1946-48 (5) 0,453 0,003 0,030 0,129 0,001 1,49 42,366 4,12963 117,292 0,100 1,187
Austr. F. 1960-62 (5) 0,552 0,002 0,032 0,132 0,000 13,95 19,839 126,49100 158,223 0,095 1,066
Austr. F. 1970-72 (5) 0,506 0,001 0,030 0,129 0,000 14,92 18,415 94,78020 156,073 0,094 0,892
Austr.M. 1946-48 (5) 0,300 0,003 0,020 0,125 0,001 9,55 20,424 0,56119 93,393 0,095 1,053
Austr.M. 1960-62 (5) 0,355 0,002 0,011 0,114 0,001 10,69 20,639 0,44044 90,119 0,099 0,947
Austr.M. 1970-72 (5) 0,413 0,002 0,011 0,110 0,002 15,24 20,055 0,40571 88,074 0,103 0,967
Valencia Region (2) 3,747 0,004 0,019 0,146 0,032 0,76 111,631 0,00036 1,005 1,716
Valencia Region (3) 2,742 0,004 0,027 0,159 0,005 6,03 23,945 90,38830 130,853 0,096
Valencia Region (4) 2,653 0,004 0,004 0,109 0,005 28,37 28,593 0,00019 1,067 1,119 4,156
Valencia Region (5) 1,476 0,004 0,006 0,116 0,005 41,12 28,794 13,38870 107,869 0,104 4,789
3. Conclusive remarks
In this paper we have proposed three models alternative to the classical nineparameters
Heligman-Pollard model expressed in (2). Of these, models (4) and (5)
achieve a better fit over the “accidental bump” region at the cost of adding one
more parameter to the second component. Models (3) and (5), in order to gain more
flexibility at older ages, employ, as third component, a logistic function with the
same number of parameters used by the exponential form in the classical model.
We test-drove our models with the original Australian datasets used by
Heligman and Pollard, and with mortality data from the Valencia Region for the
three-year period 1999–2001. When graduating Australian data, our models
showed a moderate improvement over the Heligman-Pollard model, to which it
already adapted fairly well. On the other side, on the Valencia Region dataset, our
models were able to achieve a much better fit, with an up to 60% decrease in
score over the Heligman-Pollard model.