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An Investigation of some of the Methods for deducing the Rates of Mortality, and of Withdrawal, in Years of Duration; with the Application of such Methods to the computation of the Rates experienced, and the Special Benefits granted, by Clerks' Associations (Continued)
Published online by Cambridge University Press: 18 August 2016
Extract
This subject may be conveniently considered under two headings; (1) as to the actual or assumed age at entry (2) as to the distribution of entrants and emergents over the year of duration current at entry and exit.
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- Research Article
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- Copyright © Institute and Faculty of Actuaries 1898
References
page 131 note * From some remarks made in the discussion which followed the reading of this essay, it seems necessary to point out that the limitation of the period of observation within complete calendar years is not to be confounded with the tabulation and scheduling of the facts according to the “calendar year” method. In both sections (A) and (B) of this paper the facts are tabulated according to “policy-years,” or years of duration; but in section (A) the observations included are comprised within an integral number of calendar years, the period actually selected for illustration being from 1 January 1888, to 31 December 1892.
page 134 note * I cannot entirely agree with the conclusion of Mr. Whittall (J.I.A., xxxi, 184), that this method may be classed as one of “meanages”; and Mr. King has himself expressed his dissent from this view (J.I.A., xxxi, 201). The method, as stated by Mr. King, gives, not true, but modified “mean ages”, which coincide with those arrived at by deducting the year of birth from the year of entry, in the case only where both years are reckoned from 1 July to 30 June. If, however, the method be so applied as to deduce the ages which fall on the birthdays nearest to the nearest 30 June to the dates of entry (a modification contemplated by Mr. King, J.I.A., xxvii, 218), the results will in that case precisely coincide with true “mean ages,” computed by deducting the calendar years of birth from the calendar years of entry. 1 am also unable to agree with Mr. King that the error of age can never exceed six months. This seems to me to be demonstrably inaccurate, at least, as regards the age at entry, with which alone I am now concerned; and I can only suppose that Mr. King is referring to the average error, and not to individual eases of deviation.
page 139 note * The values of (be) and (bs) are not separately stated in Schedule (E); but I have taken them from working sheets, which include the values throughout in half-years of duration.
page 147 note * See pp. 78, 79.
page 151 note * See pp. 82, 83.
page 152 note * See pp. 92, 93.
page 168 note * See pp. 71, 72.
page 170 note * For Tables I to VIII, see pages 180–6.
page 200 note * “The Evolution of Premium Rates: a chapter in the History of Life Assurance.” (Transactions of the Actuarial Society of Edinburgh, vol. iii, No. 14.)