Volume 38 - Article 29 | Pages 773–842  

Gompertz, Makeham, and Siler models explain Taylor's law in human mortality data

By Joel E. Cohen, Christina Bohk-Ewald, Roland Rau

Response Letters

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03 August 2018 | Response Letter

Why does Taylor's law in human mortality data have slope less than 2, contrary to the Gompertz model?

by Joel E. Cohen

Response by Joel E. Cohen, Christina Bohk-Ewald, Roland Rau to comments by Michel Guillot and Carl Schmertmann

The central theoretical result of Cohen, Bohk-Ewald and Rau (2018) states that the Gompertz mortality model with modal age at death increasing linearly in time obeys a cross-age-scenario of Taylor’s law (TL) exactly with slope b = 2. Guillot and Schmertmann have discovered illuminating generalizations. But, contrary to our theory and theirs, observed mortality obeys TL with a slope generally (but not in every case) less than 2. So some assumption of the mathematically correct theory is empirically wrong. Here we propose a simplified model with two age groups to identify conditions under which mortality rates obey TL with slope b < 2 or b > 2. We show that if mortality falls faster (over time) for the young than for the old, then b < 2. These conclusions raise further empirical questions.

11 July 2018 | Response Letter

More general set of conditions producing a Taylor’s Law with an exact slope of 2

by Michel Guillot

In the attached letter, I propose a set of conditions producing Taylor's Law (TL) with an exact slope of 2 that is more general than in the Cohen, Bohk-Ewald, and Rau study. This result emphasizes the importance of time trends rather than age patterns of mortality for understanding TL slopes.

11 July 2018 | Response Letter

Purely temporal variation in mortality change cannot explain deviations from TL slope=2

by Carl Schmertmann

A further generalization of Prof. Guillot's proof.

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