Comparison of the Gompertz and Weibull functions as descriptors for human mortality distributions and their intersections

Abstract

The Gompertz and Weibull functions are compared with respect to goodness-of-fit to human mortality distributions; ability to describe mortality curve intersections; and, parameter interpretation. The Gompertz function is shown to be a better descriptor for ‘all-causes’ of deaths and combined disease categories while the Weibull function is shown to be a better descriptor of purer, single causes-of-death. A modified form of the Weibull function maps directly to the inherent degrees of freedom of human mortality distributions while the Gompertz function does not. Intersections in the old-age tails of mortality are explored in the context of both functions and, in particular, the relationship between distribution intersections, and the Gompertz In[ ifR 0] versus α regression is examined. Evidence is also presented that mortality intersections are fundamental to the survivorship form and not the rate (hazard) form. Finally, comparisons are made to the parameter estimates in recent longitudinal Gompertzian analyses and the probable errors in those analyses are discussed.