Skew-t Fits to Mortality Data—Can a Gaussian-Related Distribution Replace the Gompertz–Makeham as the Basis for Mortality Studies?

Abstract

Gompertz-related distributions have dominated mortality studies for 187 years. However, nonrelated distributions also fit well to mortality data. These compete with the Gompertz and Gompertz-Makeham data when applied to data with varying extents of truncation, with no consensus as to preference. In contrast, Gaussian-related distributions are rarely applied, despite the fact that Lexis in 1879 suggested that the normal distribution itself fits well to the right of the mode. Study aims were therefore to compare skew-t fits to Human Mortality Database data, with Gompertz-nested distributions, by implementing maximum likelihood estimation functions (mle2, R package bbmle; coding given). Results showed skew-t fits obtained lower Bayesian information criterion values than Gompertz-nested distributions, applied to low-mortality country data, including 1711 and 1810 cohorts. As Gaussian-related distributions have now been found to have almost universal application to error theory, one conclusion could be that a Gaussian-related distribution might replace Gompertz-related distributions as the basis for mortality studies.

Modeling absolute differences in life expectancy with a censored skew-normal regression approach

“…The advantage of this approach over parametric survival regression techniques is that parameter estimates are directly in terms of mean life expectancy. Other underlying Gaussian-type distribution functions (i.e., the skew- t distribution or the compressed Gaussian distribution) have been investigated ( Clark et al, 2013 ; Robertson & Allison, 2012 ), with promising results in terms of model fit. In our analysis and simulation study the skew-normal distribution did not outperform the Gompertz distribution function.…”

“…Gaussian-related distribution functions have been shown to be a possible alternative to commonly used generalized extreme value distributions (e.g., Gompertz distribution) in the modeling of life expectancy ( Clark et al, 2013 ; Robertson & Allison, 2012 ; Robertson, De Los Campos & Allison, 2013 ). Clark and colleagues ( 2013 ) found that a skew- t distribution outperformed a Gompertz-like distribution function in modeling mortality data in terms of model fit. Robertson & Allison (2012) evaluated a compressed Gaussian distribution in the modeling of human longevity.…”

Dramatic differences in male and female mortality trends for selected European cohorts over ∼20 years

“…Instead of using parametric methods (e.g. gompertz, logistic, Weibull, quadratic, normal or skew-t (Clark et al, 2013)) which make some assumptions concerning underlying distributions, we follow Ouellette and Bourbeau (Nadine and Robert, 2011) and Horiuchi et al (2013) in the use of non-parametric splines. Horiuchi et al (2013) discuss the “potential theoretical importance of [the mode] in ageing research” and conclude that use of non-parametric fitting (p-splines) gave “noticeably different” modal trends to those from parametric fits (Gompertz, logistic, Weibull and their Makeham variants).…”