A Conjecture on Demographic Mortality Implies Two Asymptotic Limits for Mortality Curves in Demographic Life Tables

In a previous article, the author presented a conjecture on the trend of demographic mortality as life span progresses. This earlier article provided a mathematical formulation of the statistical distribution to which mortality would tend in this case. In the present work we show that this theory predicts that the height of the mortality peak with respect to demographic age and the amplitude at mid-height of the mortality curve itself are limited to fixed values, towards which the mortality curves will tend as the lifespan increases. These limit values are also calculated numerically. These limiting requirements derive directly from the mathematical formulation of the above said conjecture. Demographic data from the United States, Japan and Italy were used as an experimental test. For the Italian case in particular, regional subdivisions were also analyzed to see if any counterexamples to the assumed limits could emerge. In all cases, the assumed limits were not exceeded by the actual data and the apparent asymptotic trend towards these limits was confirmed by the collected data. The identified height limit also gives us a quick test for future Life Tables with 5-year age intervals: the dx data for them, in the maximum mortality interval, may not exceed 29.3% of the total cases.