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On the Adjustment of Mortality Tables

Published online by Cambridge University Press:  18 August 2016

John Adams Higham
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Extract

During the last session of the Institute of Actuaries, I had the honour to submit a paper, the purpose of which was to devise a method of adjustment as even and correct as that of Mr. Woolhouse, and more easy in application. This was to be done by combining two summations of numbers increasing by third differences; the summations being so chosen as to introduce small factors only into the formula, and to admit of its being worked in columnar shape. (Journal, vol. xxiii, page 335.)

Thereupon, Mr. G. F. Hardy showed that Mr. Woolhouse's formula can be used in columnar shape; and Mr. Ackland, improving on Mr. Hardy's arrangement, contributed a table in which an adjustment of the HM decrement was so calculated. (Journal, xxiii, 354.)

This important and unexpected result of the reading of my paper rendered it of little value, except that it supplied a short formula which may be convenient for use where a rough graduation only is required. Any degree of smoothness can be obtained by repeating the process; but this is tedious, and I would now furnish a formula derived in the same manner, and yielding a satisfactory adjustment by a single operation.

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 24 , Issue 1 , April 1883 , pp. 44 - 51
Copyright
Copyright © Institute and Faculty of Actuaries 1884

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References

page 44 note * Errata in Mr. Ackland's Table :— Age 72, col. 5, should be 30,697, and the adjusted decrement 2.503·5. Age 77, col. 5, should be 28,915, and the adjusted decrement 2,364·3. Corresponding corrections in columns 7 and 10.

page 51 note * Institute of Actuaries' Life Tables, p. xci.