A Probabilistic Framework for Estimating the Modal Age at Death

This paper introduces a novel method for estimating the empirical probability distribution of the modal age at death - the age at which the highest number of deaths occurs within a population. Traditional demographic methods often relies on point estimates derived from parametric models or smoothing techniques, which can overlook the variability and uncertainty in mortality data. By contrast, our probabilistic assessment captures this variability, providing a more comprehensive understanding of mortality patterns essential for accurate demographic forecasting and policy planning. We model death counts across discrete age intervals as outcomes of a multinomial experiment, thus aligning with the categorical nature of mortality data. A Gaussian approximation facilitates computational feasibility, allowing us to estimate modal age probabilities numerically. While our method offers a robust approach to analyzing mortality data, we acknowledge that the assumption of independent deaths may not hold in situations such as epidemics or when social factors significantly impact mortality. We discuss the scenarios where the approach holds and note any limitations in specific applications.