Threshold Ages for the Relation between Lifetime Entropy and Mortality Risk

We study the effect of a change in age-specific probability of death on risk about the duration of life measured by Shannon’s entropy defined to the base 2. We first show that a rise in the probability of death at age n increases lifetime entropy at age k≤n if and only if the quantity of information revealed by the event of a death at age n exceeds lifetime entropy at age n+1 divided by the probability to survive from age k to age n+1. There exist, under general conditions, two threshold ages: first, a low threshold age below which a rise in mortality risk decreases lifetime entropy, and above which it raises lifetime entropy; second, a high threshold age above which a rise in mortality risk reduces lifetime entropy. Using French life tables, we show that the gap between those two threshold ages has been increasing over the last two centuries.(This abstract was borrowed from another version of this item.)