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On one Uniform Law of Mortality from Birth to extreme Old Age, and on the Law of Sickness

Published online by Cambridge University Press:  18 August 2016

Benjamin Gompertz Esq.
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Extract

The honour I have received by the invitation of the President and members for organising the Fourth Session of the International Statistical Congress, to be held daring the week commencing the 16th July instant, which the state of my health prevents me having the satisfaction to attend, induces me to offer to the notice of the distinguished members some observations which, I think, may be considered of some importance in connexion with the objects of the Congress; having for many years paid attention to the subject of vital statistics, and to the mode of rendering the information derivable from its pursuit interesting, beneficially and scientifically, to the public, who may gain consoling pecuniary advantage from it, and to the student, who may enjoy the contemplation of the paths of science; because the services which have been obtained by the public from Assurance Societies, and from the proper management of Friendly Societies, have been obtained by the attentive and philanthropic study of the subject, and the mode of pursuing that study depends on statistical inquiries, and, I may say, on deep mathematical reflection,—a reflection which, whilst it may and has been of important service to society at large, may offer many new views in philosophical and mathematical branches of enquiry even quite unconnected with statistics or its objects.

Type
Research Article
Information
Journal of the Institute of Actuaries , Volume 16 , Issue 5 , October 1871 , pp. 329 - 344
Copyright
Copyright © Institute and Faculty of Actuaries 1872

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References

page 332 note * In a paper read before the Royal Society in June, 1861, the author gives ‘what he considers an improved formula’ for expressing the law of mortality, viz.:

page 340 note * Bat having mentioned the name of Registrar-General above, I consider that I ought t o state, that though lay health did not permit me to respond in the manner I should much have liked, to his courteous letter to me of 1845, I should have felt it a duty to offer my aid to his laudable wish to cause his useful labours to be aided by the labour of others.

page 341 note * Referring again to this subject in his paper of June, 1861, the author says,—“But “that this law” (i.e. the law of equal chances of survivorship) “cannot accurately exist” for any possible continuous law of mortality, I hare proved in my paper of 1825, “unless of the form La=é-e”. e a, where é, e”, e, are constant quantities at pleasure, “and a the age, and which in an extreme case of e differing infinitely little from unity, “is reducible into the form La = ǵ — g” a, if ǵ = é — e”, and g”= e” ε,— e and e” being “infinitely large, differing froma each other by a finite qnantity, and ε infinitely small, “and in consequence g” a finite quantity.”