  Trends in human longevity are puzzling, especially when considering the
limits of human longevity. Partially, the conflicting assertions are based upon
demographic evidence and the interpretation of survival and mortality curves
using the Gompertz model and the Weibull model; these models are sometimes
considered to be incomplete in describing the entire curves. In this paper a
new model is proposed to take the place of the traditional models. We directly
analysed the rectangularity (the parts of the curves being shaped like a
rectangle) of survival curves for 17 countries and for 1876-2001 in Switzerland
(it being one of the longest-lived countries) with a new model. This model is
derived from the Weibull survival function and is simply described by two
parameters, in which the shape parameter indicates 'rectangularity' and
characteristic life indicates the duration for survival to be 'exp(-1)'. The
shape parameter is essentially a function of age and it distinguishes humans
from technical devices. We find that although characteristic life has increased
up to the present time, the slope of the shape parameter for middle age has
been saturated in recent decades and that the rectangularity above
characteristic life has been suppressed, suggesting there are ultimate limits
to human longevity. The new model and subsequent findings will contribute
greatly to the interpretation and comprehension of our knowledge on the human
ageing processes.
