Note on the Inverse Relationship Between Hazard and Life Expectancy: A

Intuitively, life expectancy and hazard rate should be inversely related to each other. Whereas life expectancy, or mean time to failure, is determinable as a simple descriptive statistic, the concept o f hazard is defined as an instantaneous failure rate and involves taking limits, This note investigates "inverting" life expectancy as a method for estimating the hazard rate. The main result is that given any finite collection of (internally consistent pairs of age and associated life expectancy values, there is a uniquely determined step function that determines a "gauntlet" survival model with the given life expectancies at their respective ages. The Appendix provides a simple computer algorithm for implementing this model in practice.