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Kolmogorov-Smirnov-type test for dependently double-truncated durations: A copula approach
Anne-Marie Toparkus1, Rafael Weißbach2
1Chair of Statistics and Econometrics, Faculty for Economic and Social Sciences, University of Rostock, 18051, Rostock, Germany.
Lifetime Data Analysis
|July 18, 2026
Summary
This study introduces a new statistical test for lifespan distribution, accounting for time-varying life expectancy. The test, applied to German enterprise lifespans, clearly rejects age-homogeneous hazard rates.
Area of Science:
- Statistics
- Demography
- Survival Analysis
Background:
- Life expectancy is often nonstationary over time.
- Modeling lifespan requires accounting for dependencies like birthday.
- Double-truncated lifespan data presents unique analytical challenges.
Purpose of the Study:
- To test hypotheses about parametric lifespan distribution families.
- To model the dependence between lifespan and individual birthday using copulas.
- To develop a robust statistical test for nonstationary demographic data.
Main Methods:
- Utilized copula models, specifically the Farlie-Gumbel-Morgenstern copula.
- Employed Donsker-class arguments and the functional delta method for empirical processes.
- Developed a two-stage test involving statistic computation and critical value simulation.
Main Results:
- The proposed test demonstrated consistency under specified assumptions.
- Applied to 55,000 German enterprise lifespans, the test rejected age-homogeneous closure hazard.
- The Kolmogorov-Smirnov test provided clear evidence against an age-homogeneous model.
Conclusions:
- The developed statistical test is effective for analyzing double-truncated lifespan data.
- Findings suggest that enterprise lifespans are not homogeneous with respect to age.
- The methodology offers a framework for analyzing demographic data with time-dependent factors.
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