Modelling the age distribution of longevity leaders

TL;DR

This paper introduces a stochastic Markov model with a Poisson birth process and gamma-Gompertz lifespans to analyze the evolution of the oldest person's age, fitting historical data and predicting future trends.

Contribution

It presents a novel stochastic model for the age distribution of longevity leaders, incorporating time-dependent parameters and providing future age distribution estimates.

Findings

Model fits historical data well

Oldest age is projected to increase over time

Parameters enable future age distribution predictions

Abstract

Human 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.