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On Interpolation, Summation and the Adjustment of Numerical Tables. (Part III)

Published online by Cambridge University Press:  18 August 2016

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

Extract

When a series of quantities which depend on a fixed law, whether known or implied, follow each other in a due order of succession, the general accuracy of their numerical values may be satisfactorily tested by observing the regularity of the progression of a suitable order of differences. If the tabular quantities are the results of calculation from a given formula, with equidistant arguments, by differencing them up to a certain order the existence of an isolated error, if one should exist, is thus prominently exhibited and therefore speedily detected. Moreover the precise locality of the error and the fact of its individuality being indicated by a characteristic interruption of the law of progression, the proper correction is ascertained by carefully noting the central position of the disturbance, and revising the corresponding portion of the original computation. This work of revision may, however, be dispensed with, if necessary or desirable, as the magnitude as well as the locality of the indicated error can in general be readily deduced, with sufficient accuracy, directly from the differences, by the method of adjustment here given. The method, being so far independent of fundamental origin, is therefore equally applicable to the adjustment of a series of quantities derived from observation, or from statistical data; only in this latter case, as almost every quantity must be more or less affected by imperfections arising from defective information and other known or unknown incidental causes, the influence of which may sometimes be augmented by paucity of numbers, the progression of the differences is disturbed by a more complicated combination of the effects of an irregular series of errors, and it becomes more difficult to eliminate the value of each separate correction.

Type
Research Article
Copyright
Copyright © Institute and Faculty of Actuaries 1866

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References

page 142 note *Investigationof Mortality in the Indian Army. By W. S. B. Woolhouse, F.R.A S., &c.,” and “Tables Exhibiting the Law of Mortality deduced from the Combined Experience of Seventeen Life Assurance Offices.” It is presumed that no existing graduated table of mortality represents so closely the general body of facts on which it is founded as the tables here referred to. Mr, Jellicoe, the President of the Institute, at the end of a valuable paper inserted in vol. 1., page 166, has given a D and N table, together with the values of an annuity and annual premium, calculated from the adjusted Bengal Military Mortality, at 4 per cent.

page 156 note † The numbers k put on a separate slip may be mechanically placed in position upon the other table, and thus all transcription will be dispensed with.