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Threshold dynamics in age-structured distributions with expanding support: A unified mathematical framework.
1Institute of Population Studies, Fudan University, Shanghai, 200433, China.
Theoretical Population Biology
|June 22, 2026
Summary
Threshold ages in mortality studies shift towards younger ages as the maximum observed age expands. This finding impacts lifespan variation analysis and demographic transition research.
Area of Science:
- Demography
- Biostatistics
- Actuarial Science
Background:
- Threshold ages define shifts in mortality reductions affecting lifespan variation.
- Classical models assume a fixed lifespan, but empirical data uses expanding maximum ages.
- Understanding threshold dynamics under evolving lifespans is crucial.
Purpose of the Study:
- Develop a unified framework for threshold age dynamics with expanding lifespan support.
- Analyze the impact of expanding maximum observed age on threshold ages.
- Provide a general formula for threshold shifts.
Main Methods:
- Scale-shape decomposition of spread measures.
- Sensitivity decomposition into shape and domain-scaling channels.
- Derivation of a normalized threshold formula (y* = x*/ω).
Main Results:
- The domain-scaling channel shifts thresholds to younger ages as maximum observed age (ω) increases.
- Normalized thresholds (y*) provide a consistent measure across different maximum ages.
- Historical data shows significant evolution of normalized thresholds during demographic transitions.
Conclusions:
- The proposed framework accurately captures threshold dynamics under expanding lifespans.
- The domain-scaling effect is a key factor influencing threshold age shifts.
- Findings have implications for understanding population aging and demographic change.
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