10.57647/mathsci.2026.2004.21

Survival Analysis Based on the AFT Approach with a Semi-Continuous Response under Zero-Inflation:An Application in Life Insurance

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  • Nafiseh Khojasteh Bakht1,
  • Shirin Shoaee*1,
  • Ehsan Bahrami Samani2,
  1. Department of Actuarial Science, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
  2. Department of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

Received: 2025-11-14

Revised: 2026-04-04

Accepted: 2026-05-06

Published Online: 2026-05-25

Copyright (c) 2026 Nafiseh Khojasteh Bakht, Shirin Shoaee, Ehsan Bahrami Samani (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Khojasteh Bakht, N., Shoaee, S., & Bahrami Samani, E. (2026). Survival Analysis Based on the AFT Approach with a Semi-Continuous Response under Zero-Inflation:An Application in Life Insurance. Mathematical Sciences. https://doi.org/10.57647/mathsci.2026.2004.21
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Abstract

Mortality models in actuarial science are important tools used to develop models from historical data to predict future trends and mortality rates, particularly in life insurance and premium assessments. These models need to be flexible enough to accommodate effects such as age and product type. Censoring also features as a unique element providing a basis for survival analysis, as it is not very often that the entire duration values are present as non-negative or asymmetric for various censored cases. Standard regression methods are unsuitable for such data, and specialized techniques such as Cox Proportional Hazards and Accelerated Failure Time (AFT) models are required. AFT models allow for flexible distributional assumptions while providing interpretable results in complex settings.

This study extends the AFT framework by introducing a Zero-Inflation compo-nent to accommodate semi-continuous lifetime data characterized by excess zeros, thereby transforming a purely continuous distribution into a semi-continuous one. By integrating zero inflation with both right- and left-censoring mechanisms, the proposed models expand the applicability of survival analysis in actuarial contexts.

The empirical analysis is based on a real dataset obtained from a medium-sized pension fund, including individual-level information on future lifetimes and relevant covariates. The results demonstrate that the zero-inflated Gompertz AFT model provides superior performance compared to competing specifications, particularly in capturing tail behavior and age-dependent mortality dynamics. Furthermore, the inclusion of zero inflation significantly improves model flexi-bility and estimation accuracy in the presence of excess-zero observations. From an actuarial perspective, the proposed modelling framework offers improved estimation of survival patterns and annuity factors, supporting more accurate longevity risk assessment and better-informed decision-making in life insurance and pension applications.

Keywords

  • Future LifeTime Variable,
  • Zero-Inflation,
  • Accelerated Failure Time (AFT),
  • Analysis, Annuity Factor
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