  Accurate demographic functions help scientists define and understand
longevity. We summarize a new demographic model, the Weon model, and show the
application to the demographic data for Switzerland (1876-2002). Particularly,
the Weon model simply defines the maximum longevity, which is induced in nature
by the mortality dynamics. In this study, we reconsider the definition of the
maximum longevity and the effectiveness for longevity by the combined effect of
the survival and mortality functions. The results suggest that the mortality
function should be zero at the maximum longevity, since the density function is
zero but the survival function is not zero. Furthermore, the effectiveness for
longevity can be maximized at the characteristic life by the complementarity
between the survival and mortality functions, which suggests that there may be
two parts of rectangularization for longevity. The historical trends for
Switzerland (1876-2002) implies that there may be a fundamental limiting force
to restrict the increase of the effectiveness. As a result, it seems that the
density function is essential to define and understand the mortality dynamics,
the maximum longevity, the effectiveness for longevity, the paradigm of
rectangularization and the historical trends of the effectiveness by the
complementarity between the survival and mortality functions.
