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Summary
This study introduces a mathematical model to calculate cohort mortality trends from period data. It enables the derivation of cohort survivorship functions, even with gradual mortality changes, given an estimate of the mortality change.
Area of Science:
- Demography
- Mathematical Modeling
- Biostatistics
Background:
- Period life tables and forces of mortality are standard demographic tools.
- Estimating cohort-specific mortality from period data is challenging, especially with changing mortality rates.
- Understanding cohort mortality is crucial for long-term population studies and actuarial science.
Purpose of the Study:
- To develop a mathematical model for deriving cohort mortality functions from period data.
- To enable the estimation of cohort forces of mortality and survivorship functions.
- To provide a method for analyzing mortality under gradually changing conditions.
Main Methods:
- Development of a functional mathematical model.
- Application of the model to period force of mortality and period life table data.
- Derivation of cohort functions using an estimate of mortality change.
Main Results:
- A method to derive cohort forces of mortality from period data is presented.
- Cohort survivorship functions can be obtained under gradually changing mortality.
- An example demonstrates the successful derivation of cohort functions.
Conclusions:
- The proposed mathematical model effectively translates period mortality data into cohort-specific metrics.
- This approach is valuable for demographic analysis when mortality patterns evolve over time.
- The model provides a robust framework for actuarial and epidemiological studies.