Cultural imagery and statistical models of the force of mortality, and a new (old?) way to make the link between its integral and the survival function
We describe selected artistic and statistical depictions of the force of mortality [hazard or mortality rate], a concept that has long pre-occupied actuaries, demographers and statisticians. We provide a more graphic form for the force of mortality function that makes the relationship between its constituents more explicit.
The "Bridge of Human Life" in Addison's (1711) allegorical essay provides a particularly vivid image, with the forces depicted as external. The model used by Gompertz (1825) appears to treat the forces as internal.
In his 1897 essay Pearson mathematically modernises "the medieval conception of the relation between Death and Chance" by decomposing the full mortality curve into five distributions along the age axis, the results of five "marksmen" aiming at the human mass crossing this bridge.
We describe Addison's imagery; comment briefly on Gompertz's law and the origin of the term 'force of mortality'; describe the background for Pearson's essay, as well as his imagery and statistical model; and give the Bridge of Life a modern form, illustrating it via statistical animation.
We use Edmonds' (1832) concept of person-time, and the Poisson distribution, to provide a new (old?) way to make the link between the integral of the hazard function and the survival function.