Location-Scale Models in Demography: A Useful Re-parameterization of Mortality Models

Area of Science:

• Demography
• Actuarial Science
• Biostatistics

Background:

• Parametric mortality models are essential for understanding age-specific mortality patterns.
• Existing models lack a unified framework for comparison and analysis.
• Gompertz's law of mortality established early foundations for these models.

Purpose of the Study:

• To demonstrate that numerous mortality models can be unified within a single location-scale (LS) framework.
• To introduce the demographic interpretability of LS parameters (location and scale).
• To highlight the statistical and interpretability advantages of the LS parameterization.

Main Methods:

• Re-parameterization of existing mortality models into the location-scale (LS) family.
• Statistical estimation of LS parameters.
• Comparative analysis using illustrations from the Human Mortality Database.

Main Results:

• Many demographic and actuarial mortality models are shown to be re-parameterizable within the LS family.
• LS parameters offer direct demographic interpretations of mortality shifts and compression.
• LS parameter estimation exhibits lower correlation, reducing bias and enhancing interpretability.

Conclusions:

• The location-scale (LS) family provides a flexible and unified framework for parametric mortality modeling.
• LS parameterization enhances the interpretability, comparability, and statistical estimation of mortality models.
• This approach offers significant advantages over traditional parameterizations in demographic and actuarial research.