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Notes on graduation

Published online by Cambridge University Press:  07 November 2014

James Buchanan
James Buchanan
Affiliation:
Government Actuary's Department
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Extract

Few actuaries are required to deal with problems of graduation, and some may be inclined to regard the subject-matter of this paper as highly unpractical; nevertheless it had its origin in questions which presented themselves for solution in the course of everyday work. Some may even be disposed to regard graduation as a kind of juggling with figures, the results of which have to be taken on trust; and they have a certain amount of justification in that the processes are not always fully explained. To satisfy these doubts full details of the methods employed are given in the Appendix, and one or two examples are completely worked out, so that students will be enabled to follow the process from beginning to end.

Type
Other
Information
Transactions of the Faculty of Actuaries , Volume 10 , 1925 , pp. 289 - 343
Copyright
Copyright © Institute and Faculty of Actuaries 1925

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References

page 291 note * It must be remembered that the experience is one of policies, not lives. Cases were frequent in which there were many contracts on the same life, and, according as the mortality in any year of age happened to fall mainly on lives insured under single or multiple contracts, there would be large deviations on one side or the other of the smooth curve. This can be seen at once by reference to the ungraduated data in Table IX. of the Report. The regrouping of the data was resorted to so as to bring into the same groups as far as possible balancing irregularities of this kind.

page 293 note * There is a misprint in Table IX. The exposed to risk at age 88 should be 3422, not 3432.

page 294 note * Cf. The Calculus of Observations: Whittaker and Robinson, p. 369.

page 294 note † Cf. “Note on the Possibility of the Division of the Law of Mortality into Geometrical Series”: W. S. B. Woolhouse. J.I.A. xi. p. 150.

page 296 note * Cf. Report for 1912-13 on the Administration of the National Insurance Act, Part I., Health Insurance—Cd. 6907—pp. 595-7.

page 302 note * Census of England and Wales, 1911, vol. vii., ‘Ages and Condition as to Marriage’—Cd. 6610—p. lii.

page 328 note * Cf. J.I.A., vol. xlvi. pp. 1-64 and 168-193: also Austin and Symmons, Joint Life Tables, pp. iii-iv.