Some Illustrations of the Employment of Summation Formulas in the Graduation of Mortality Tables

Extract

Mr. George King's recent investigation of the magnitude of the error introduced into certain functions of a mortality table following Makeham's law when these are re-graduated by summation formulas (J.I.A., xli, 54), has again attracted attention to the subject of the graduation of mortality tables, and has recalled the lively controversy which took place some years ago between Dr. Sprague and the late Mr. Woolhouse over the merits and demerits of the methods championed by those distinguished authorities. Not the least interesting contribution to the discussion which followed the reading of Mr. King's paper was furnished by Dr. Sprague himself, who wrote in defence of certain criticisms expressed by him with regard to methods of summation generally and Mr. Woolhouse's formula in particular. Dr. Sprague remarked that he had “objected to Mr. Woolhouse's “formula of graduation,on two grounds, which it has in common “with all other summation formulas; that is to say, (1) because “it does not remove the irregularities of the original series of “facts, but only reduces them, and (2) because it distorts the “law of the facts to a greater or less extent.” He went on to say that the results of his re-graduation of the H^M (Text-Book) Table by Woolhouse's formula had led him to the conclusion that the second objection might be disregarded in practice, but that there still remained objection (1), which he considered by far the more important.