Distributions of Age at Death from Roman Epitaph Inscriptions: An Application of Data Mining

Abstract

Thousands of age at death inscriptions from Roman epitaphs are statistically analyzed. The Gompertz distribution is used to estimate survivor functions. The smoothed distributions are classified according to the estimation results. Similarities and differences can be detected more easily. Parameters such as mean, mode, skewness, and kurtosis are calculated. Cluster analysis provides three typical distributions. The analysis of the force of mortality function of the three clusters yields that the epigraphic sample is not representative of the mortality in the Roman Empire. However, the data is not worthless. It can be used to show and to explain the differences in the burial and commemorative processes. Finally, the bias due to a growing population is discussed. A simple formula is proposed for estimating the growth rate. The paper also discusses some special parameter constellations of the Gompertz distribution, since in this special application it cannot be approximated by the Gumbel distribution (as is often done in life table analysis).