Graunt, Halley, and US 1993 Life Table with ggplot
Peter Mwandri
13 April 2016
Source of Data
Graunt’s Life Table
The area under the curve can be approximated by the sum of the areas of trapezoids, therefore the area is \(\sum_{i=1}^{n-1} (x_{i+1}-x_i)\times\frac{1}{2}(y_i + y_{i+1})\). Therefore, the life expectancy of Graunt’s life table is 18.17(years).
Comparison with US 1993 life table
The shaded area between the survival function of Graunt and that of US 1993 represents the difference of life expectancies.
The area under the US 1993 survival function is 70.92, so, the area of shaded region, that is the difference of life expectancy, is 52.75 (years).
Comparison with Halley’s life table
| age | lx | xPo | age | lx | xPo |
|---|---|---|---|---|---|
| 0 | 1238 | 100.0 | 75 | 88 | 7.1 |
| 1 | 1000 | 80.8 | 76 | 78 | 6.3 |
| 2 | 855 | 69.1 | 77 | 68 | 5.5 |
| 3 | 798 | 64.5 | 78 | 58 | 4.7 |
| 4 | 760 | 61.4 | 79 | 50 | 4.0 |
| 5 | 732 | 59.1 | 80 | 41 | 3.3 |
| 6 | 710 | 57.4 | 81 | 34 | 2.7 |
| 7 | 692 | 55.9 | 82 | 28 | 2.3 |
| 8 | 680 | 54.9 | 83 | 23 | 1.9 |
| 9 | 670 | 54.1 | 84 | 20 | 1.6 |
R base graphics
Compute the difference of life expectancies, Halley’s is 27.872 (years), and Graunt’s is 18.17 (years).
Graunt, Halley, and US 1993
ggplot
Graunt
Graunt and US 1993
Graunt and Halley
Graunt, Halley, and US93
