# Threshold ages for the relation between lifetime entropy and mortality risk

*Patrick Meyer* and
*Gregory Ponthiere* ()

*Mathematical Social Sciences*, 2020, vol. 108, issue C, 1-7

**Abstract:**
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.

**Keywords:** Mortality risk; Lifetime entropy; Threshold age (search for similar items in EconPapers)

**Date:** 2020

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**Related works:**

Working Paper: Threshold Ages for the Relation between Lifetime Entropy and Mortality Risk (2019)

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:matsoc:v:108:y:2020:i:c:p:1-7

**DOI:** 10.1016/j.mathsocsci.2020.07.004

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