A Probabilistic Framework for Estimating the Modal Age at Death

We present a novel method for estimating the probability distribution of the modal age at death - the age at which the highest number of deaths occurs in a population. Traditional demographic methods often relies on point estimates derived from parametric models or smoothing techniques, which may overlook the inherent variability and uncertainty in mortality data. By contrast, our approach models death counts across age intervals as outcomes of a multinomial distribution, aligning with the categorical nature of mortality data. By applying a Gaussian approximation, we make the computation of modal age probabilities feasible. While this probabilistic method offers a robust approach to analyzing mortality data, we acknowledge its limitations, particularly the assumption of independent deaths, which may not hold during events like epidemics or when social factors significantly influence mortality.