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On the Construction of Tables of Mortality

Published online by Cambridge University Press:  18 August 2016

W. S. B. Woolhouse*
Affiliation:
Institute of Actuaries, &c.

Extract

A Table of mortality is designed to represent the number of lives which, according to the best deductions from past experience, may be expected to survive at the termination of each successive year of age, supposing these survivors to be derived exclusively from a certain number of persons originally taken either at birth or at a given age. As a practical index of the mathematical law of average mortality such a table may be taken as a trustworthy guide for the future, provided that the number of lives which enter into its formation be sufficiently large and the particulars respecting them be correctly registered; and, what is equally important, that the observations shall extend over a considerable number of years.

Type
Research Article
Copyright
Copyright © Institute and Faculty of Actuaries 1867

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References

page 82 note * See the Form on page 77.

page 82 note † An increased facility has recently been given to the processes of analysing the facts of a mortality experience by simply conveying the original particulars, with respect to each individual life, upon a separate card, specially designed to receive them. By this means the object of classifying each particular element, whatever it may be, is accomplished by the purely mechanical operation of shuffling the cards into the required order, without incurring the necessity, in any case, of making preliminary extracts of the several details. This is, undoubtedly, the most prominent advantage obtained, as there is always a much greater liability to error in making long and tedious transcriptions than in performing the operations of calculation. The plan, here briefly described, was first made publicly known in “An Account of the Processes employed in getting out the Mortality Experience of the Economic Life Assurance Society,” and was the suggestion of Mr. O. G. Downes, of that Office. An appropriate and well-considered form of card, calculated to meet every requirement and convenience, is presented in the pamphlet referred to, and the method is appropriately designated the “card system.” It is also pointed out that “it affords the means of making any deductions required, as it is only necessary to throw the cards into hotch-potch, and then rearrange them in the order needed to accomplish the required object—a process which would afford pleasant fireside amusement to any domesticated actuary and his family.”The only disadvantage that could attend the method would appear to be the possibility of some of the cards, in their dignified isolation and independence, getting accidentally astray from the general mass, and carrying with them their separate contents, a casualty which could not happen when the materials are permanently entered on sheets, prepared for their reception. The mere idea of this supposed objection will, at least, induce a due amount of caution in those who, in the discussion of any branch of statistics, may be disposed to avail themselves of the manifold advantages of the card system.

page 85 note * The average interval by which the date of entry precedes the birthday is here assumed to be half a year, which may be expected to be somewhat in excess, since in some cases it is natural to surmise a disposition to expedite an assurance when a coming birthday, in near perspective, is suggestive of a higher rate of premium. According to actual experience the average interval is found to be about three-eighths of a year. The difference is however not material. As the lives are by this means accounted nearly one-eighth of a year younger than they really are, the ultimate tendency will be to slightly increase the rate of mortality. A more accurate method of computation is given further on.

page 101 note * It will be observed that Mr. Jellicoe, in his investigation just referred to, has not failed, with the exercise of tact and discrimination, to effect a practical remedy for the defective continuity observable at these points.