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Temporary Assurances
Published online by Cambridge University Press: 18 August 2016
Extract
The subject of Temporary Assurances has been suggested as one that would be of interest to Members of the Institute of Actuaries, and the present paper is an attempt to examine the mortality among lives who have been assured by this class of policy. All the particulars that have been used are given in the “Combined Experience of Assured Lives—Endowment Assurances and Minor Classes of Assurance” (C. & E. Layton, 1900), but for convenience of reference Table I has been extracted and gives the experience in a slightly altered form for the durations 0–4 years, and Table II shows the groups into which the data were thrown so as to render them less uneven. The reason for omitting the experience beyond duration “4” was that it is generally assumed for practical purposes that selection has worn off by that time.
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- Copyright © Institute and Faculty of Actuaries 1903
References
page 502 note * Mr. Lidstone's suggested method for graduating a small Table was considered, but it seems to force the small Table into the form of the larger one from which the ratios are obtained. It was also difficult to find a suitable Table on which to work. I am doubtful if the method is sound unless the small Table is of such a description that it might be considered as a random sample from the larger Table.
page 503 note ‡ “Skew Variation in Homogeneous Material” (Phil. Trans., 1895, Vol. 186A, pp. 343, &c ).
page 503 note ‖ J.I.A., xxxiii, p. 531.
page 504 note * It is also worth noting that if 
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page 504 note † In practice we calculate the moments about some central point so as to avoid fractions and then make adjustments to get the moments about the mean.
page 504 note ‡ Proc. London Math. Soc., Vol. XXIX, p. 368. Prof. Pearson has since given a general solution in Biometrika, Part III, Vol. I.
page 506 note * For a full description of the method and of the equations by which the constants are obtained from the moments, reference must be made to Professor Pearson's papers quoted above. The following may also be referred to for examples, &c.: Pearson & Filon, “Probable Errors of Frequency Constants”, Phil. Trans., 1897; Pearson & Lee, “Distribution of Frequency of the Barometric Height, &c.”, Phil. Trans., 1898; Yule, “History of Pauperism”, Journal Statistical Society, Vol. LIX; and Pearson, “Chances of Death.” Since this paper was written Professor Pearson has dealt with Systematic Curve Fitting, see Biometrika, Vol. I, Part III, and Vol. II, Part I.
page 508 note * This periodical, the first number of which appeared in October 1901, is published four times a year by the Cambridge University Press. It contains much that should be of great interest to actuaries, and it is hoped that the Institute may see its way to add it to the library.
page 508 note † Two examples of the method with all the working will be found in Tables XI and XII.