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On the Laws of Sickness and Invalidism; and their relation to the Law of Mortality

Published online by Cambridge University Press:  18 August 2016

W. M. Makeham*
Affiliation:
Institute of Actuaries

Extract

In a paper read before this Institute many years ago, by Mr. S. Brown, occur the following judicious remarks relative to Statistics of Mortality and Sickness:—

“It has frequently been remarked” says Mr. Brown, “that “however varied and uncertain may be the occurrence of the events “to which the life of a single individual is exposed, the average “return in a large mass of persons is so regular as to be predicted “with confidence within very small limits of error. On the “uniform happening of these events under similar circumstances, “or the discovery of the laws by which they are governed, the “actuary depends for the application of the theories of probabilities “to the many useful purposes for which they may be rendered “available. The principal difficulty which he has to encounter is “the indefinite character of the event itself. In endeavouring to “ascertain the law of mortality at any period of time, or in any “particular country, the event is certain and definite whenever it “does occur. The attention is only required to the difference of “the circumstances which cause it—the age of the party, the “nature of the disease, or the locality within certain boundaries of “which a greater or less intensity of disease may prevail. But a “much greater difficulty arises when the event itself which is under “observation is of an uncertain character; such for instance as the “average duration or effects of sickness in a large number of cases.

Type
Research Article
Copyright
Copyright © Institute and Faculty of Actuaries 1872

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References

page 409 note * “On the Uniform Action of the Human Will, as exhibited by its Mean Result in Social Statistics.” By Brown, Samuel, Esq. Assurance Magazine, vol. ii page 341.Google Scholar

page 411 note * It is too often forgotten, at least by English actuaries, that all Tables of Mortality are necessarily “hypothetical” when applied to determine the future mortality in a constantly changing body of individuals brought together like the members of an Assurance Society.

page 412 note * Sx is the number of persons sick at the exact age oc, of whom some die in the year, and others recover, their places being taken by others of the healthy, some of whom, again, die, and so on, in the course of the (x+ 1)th year.

page 414 note * For the reason already stated I have not thought it necessary to resort to any very elaborate processes for determining these values.

page 415 note * A similar objection applies to Gompertz's hypothesis of sickness, viz., log σx a + b. ex (See Journal, vol. xvi p. 342). After a certain extreme age the average number of weeks' sickness in the year will exceed the number of weeks in the year.