At modal age at death, the hazard rate is determined by its derivative

The relation between the hazard rate and its derivative at modal age at death, an equivalent to which has been featured by Pollard (1991), Canudas-Romo (2008), Thatcher et al. (2010), and Tuljapurkar and Edwards (2011), is presented as a handy tool in studying mortality compression in its period and cohort dimensions. Our analytical findings indicate birth cohorts to differ substantially from the period life tables with respect to the distribution of deaths around the mode. Empirical results support theoretical predictions and show that previously reported effect of compression of deaths above the mode might be a feature of period life tables and not of the cohort mortality schedules. Our results are also useful in computing the modal age at death and sensitivity analysis.