Lois de mortalité et age limite

Abstract

Hervé Le Bras. Laws of Mortality and the Life Span. In any quantitative discussion of mortality the idea of a « limiting age » or life span must either be accepted or rejected. Past writers on these two subjects have often neglected the link between mortality levels and the life span. The so-called « laws » of Gompertz and Makeham are not proper laws, for lognormal and Gamma distributions can also be fitted to mortality data and provide a good description. Gumbel's paradox, that life tables with higher levels 'of mortality lead to more people surviving to old age is consistent with the phenomenon of the convergence of Gompertz lines which has been noted in many life tables. However, it is doubtful whether the age at which these lines converge may be regarded as the life span. There seems to be no reason to believe that log qx is a linear function of x only when age is measured in individual years. And if qx = 1 denotes the certainty of dying before birthday jc + 1, a value of unity cannot have a meaning for a force of mortality. Lastly, it is impossible to provide a proof for the existence of a limiting age, but it is clear that some graduations of mortality contain a parameter which may be interpreted as being the limiting age.

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