The Theory of the Construction of Tables of Mortality And of Similar Statistical Tables in Use By the Actuary. a Course of Lectures

George Francis Hardy

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This method is also useful if one or both limits to the range of the curve can be assumed.
Consider a scheme such as the following, in which, with a view to clearness, we use actual numbers of the series, given on p. 53, instead of symbols : — X «a 2«a: 2^« 2%x 2V 2*«, «a;Xay* 1 729 ...
...
1 2 8 12 60 160" 728 716 656 2,916 2,188 1,472 7.776 (6,318) 4,860 2,672 9,180 4,820 15,660 (11,070) 6,480 12 960 12,960 4 240 496 816 1,200 1,648 2,160 61,440 5 192 256 820 384 448 512 120,000 6 64 64 64 64... 64 64 82,941 278,316 In this scheme, each column is formed from the preceding by successive addition from the bottom, in the same way that the M^? column is formed from Q>x , and Ea- from Ma?.
If we take the value against aj=0 in the column Xux, say Xuo, we see that each value of u^ occurs once only in that total. In the total appearing against aj=l in the second summation, say S^i, each value of Ua, occurs x times; similarly the total against aj=2 in the column X^Ua?, say S®W2 } represents the sum of the products x(x—l) Ux\ and the Digitized by VjOOQ IC 60 total against a?

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