# Deriving and comparing healthy longevity distributions by gender and health prevalence measures: a statistical moments and maximum entropy approach

## TL;DR

This study compares how long men and women stay healthy past age 60 using statistical methods to analyze health data from European surveys.

## Contribution

The study introduces formal comparisons of healthy longevity distributions using the healthy lifespan outsurvival statistic and Hellinger distance for the first time in this field.

## Key findings

- Females generally have longer healthy life expectancy and less dispersed distributions compared to males.
- Males have a higher probability of health loss at younger ages and lower chances of outliving females in most health measures.
- The most similar healthy longevity distributions between genders were observed for life free of chronic conditions.

## Abstract

The literature on healthy longevity has typically focused on average values (i.e., healthy life expectancy). Recent studies have started to expand this focus by investigating the whole healthy lifespan distribution, especially the standard deviation of healthy longevity, which captures inter-individual variation. Despite these advancements, research gaps remain on how distributions differ by health indicator and sex. This study aimed to compare healthy longevity distributions at age 60 between different health measures and sexes.

We used data from the Survey of Health, Ageing and Retirement in Europe and the Human Mortality Database. A Markov chain model was used to estimate the first three statistical moments of healthy longevity distributions. The maximum entropy method was then applied to derive the full distributions. The healthy lifespan outsurvival statistic and the Hellinger distance were used to compare distributions between males and females.

For most health measures, the probabilities of health loss at younger ages were higher for males than for females, and females had a longer healthy life expectancy. Males had more dispersed distributions with a lower mode. For most health measures, healthy longevity distributions were negatively skewed, with a mode age (i.e., the age with the highest probability of health loss) higher than the healthy life expectancy age. The probability for a man to have a longer healthy lifespan than a female was below 50% for various health measures and was the lowest for living free of cardiovascular disease. In contrast, the probability for a man to live free of arthritis or rheumatism for longer than a female was above 50%. The most similar distributions between males and females were observed with life free of any chronic conditions and life with no more than one chronic condition.

This study extended the scope of healthy longevity research by complementing a focus on the statistical moments with observations on the mode of the distributions and with formal comparisons based on the healthy lifespan outsurvival statistic and the Hellinger distance, which are applied for the first time in the healthy longevity field.

The online version contains supplementary material available at 10.1186/s12963-026-00470-9.