Author:
Kiss Csaba,Németh László,Vető Bálint
Abstract
AbstractHuman longevity leaders with remarkably long lifespan play a crucial role in the advancement of longevity research. In this paper, we propose a stochastic model to describe the evolution of the age of the oldest person in the world by a Markov process, in which we assume that the births of the individuals follow a Poisson process with increasing intensity, lifespans of individuals are independent and can be characterized by a gamma–Gompertz distribution with time-dependent parameters. We utilize a dataset of the world’s oldest person title holders since 1955, and we compute the maximum likelihood estimate for the parameters iteratively by numerical integration. Based on our preliminary estimates, the model provides a good fit to the data and shows that the age of the oldest person alive increases over time in the future. The estimated parameters enable us to describe the distribution of the age of the record holder process at a future time point.
Funder
National Research, Development and Innovation Office
Deutsche Forschungsgemeinschaft
Max Planck Institute for Demographic Research
Publisher
Springer Science and Business Media LLC
Reference29 articles.
1. Oeppen, J. & Vaupel, J. W. Broken limits to life expectancy. Science 296, 1029–1031 (2002).
2. Canudas-Romo, V. Three measures of longevity: Time trends and record values. Demography 47, 299–312 (2010).
3. Vaupel, J. W., Villavicencio, F. & Bergeron-Boucher, M.-P. Demographic perspectives on the rise of longevity. Proc. Natl. Acad. Sci. 118, e2019536118 (2021).
4. Gompertz, B. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philos. Trans. R. Soc. Lond. 115, 513–583 (1825).
5. Németh, L. & Missov, T. I. Adequate life-expectancy reconstruction for adult human mortality data. Plos One 13, e0198485 (2018).