A statistical distribution with an unbounded hazard function and its application to a theory from demography

Area of Science:

• Demography
• Biostatistics
• Survival Analysis

Background:

• Aging processes are complex and not fully captured by existing statistical models.
• Demographic theories suggest specific patterns in aging and mortality.
• Understanding human lifespan limits requires advanced statistical tools.

Purpose of the Study:

• Introduce a new statistical distribution inspired by demographic aging theory.
• Investigate the properties and parameter estimation of this novel distribution.
• Apply the distribution to estimate a finite limit on human lifespan.

Main Methods:

• Defined a new statistical distribution with a hazard function proportional to (psi-t)beta-1.
• Derived properties and maximum likelihood estimates for the distribution's parameters.
• Utilized mixture distributions to model heterogeneous populations.
• Compared the new model with Gompertz and generalized Pareto distributions.
• Applied the model to survival data of female centenarians.

Main Results:

• The proposed distribution exhibits unique properties suitable for modeling aging.
• Maximum likelihood estimation provides reliable parameter estimates.
• Mixture models effectively handle population heterogeneity.
• The model successfully estimated a finite limit on human lifespan from centenarian data.

Conclusions:

• The new statistical distribution offers a valuable tool for aging research and survival analysis.
• The findings suggest a potential finite limit to human lifespan.
• This model provides a framework for analyzing survival in specific populations, like centenarians.