Modeling human population death rates: a bi–dimensional stochastic Gompertz model with correlated Wiener processes

Abstract

This study presents an innovative approach to human mortality data analysis, namely a transversal analysis across time using stochastic differential equation models, as a form of considering random environmental oscillations on the death rates. For each age between 0 and 99, we use a bi-dimensional stochastic Gompertz model with correlated Wiener processes to model the dynamics of female (first component of the stochastic process) and male (second component) crude death rates of the Portuguese population over the period 1940–2009. We test the complete model, with correlation between the unidimensional Wiener processes associated with males and with females, against the model without correlation effects. Results show significant correlations for most ages, particularly on ages below 5 and above 50.