Supplementary material from "The Evolving Statistical Signature of Human Mortality: Skewness, Kurtosis, and Life Span Disparity"

Life span disparity, a measure of variation in ages at death, can be expressed as a linear combination of standard measures of statistical dispersion in age-at-death distributions (e.g., skewness). Using data from the Human Mortality Database (7,408 life tables from 41 countries, 1751–2019), we conduct an empirical analysis of this mathematical result and assess the extent to which the moments of age-at-death distributions determine and drive life span disparity and trends in it. We report four findings: (1) remaining life expectancy contributes most to life span disparity, but its share has declined over time as the variance, skewness, and kurtosis constitute larger shares; (2) changes in skew of the age-at-death distributions have shifted and compressed mortality: distributions including older (younger) ages show increasingly positive (negative) skewness –left-leaning (right-leaning) distributions, with recent trends toward symmetric distributions; (3) kurtosis patterns show a persistent fraction of deaths remaining at distribution extremes suggesting a plateau in the number of centenarians; and (4) for adult populations (e.g., aged 30+), about 95\% of life disparity values are determined from the first four standardized moments of the associated age-at-death distributions. Incorporating skewness and kurtosis yields new insights into mortality compression and life span variability trends.