Learning Weibull Loss Severity Models From Truncated And Censored Data

Author

• Majed Alkhasha, University of Central FloridaFollow

ORCID

0009-0000-9980-6159

Keywords

Weibull loss severity models, Truncated and censored data, Maximum likelihood estimation, Method of trimmed moments, Insurance loss modeling, Payment-per-loss and payment-per-payment models.

Subject Categories

Applied Statistics | Mathematics | Other Statistics and Probability

Abstract

In modern actuarial science and risk management, due to various loss control mechanisms, observed severity losses are typically left-truncated at the deductible, right-censored at the policy limit, and scaled by a pre-specified co-insurance factor. This results in two types of actuarial payment random variables: payment-per-payment (PPP) and payment-per-loss (PPL). To learn ground-up Weibull loss severity models from PPP and PPL sample data, we implement two estimation techniques: Maximum Likelihood Estimation (MLE) and the dynamic Method of Trimmed Moments (MTM). MLE is employed to obtain efficient estimates of the Weibull shape and scale parameters. However, MLE may assign unnecessarily large point mass at the truncation or censoring points, rendering the fitted ground-up loss model sensitive to small perturbations in the underlying assumptions. To address this limitation and to develop more stable severity models with bounded influence functions, we explore the general MTM approach under both PPP and PPL data scenarios. MTM reduces the impact of extreme values by trimming a small fraction of the most influential observations, effectively eliminating undue point mass at the truncation and censoring points. This yields a balanced trade-off between bias and variance. For inferential justification, we derive the asymptotic distributional properties of both MTM and MLE estimators under PPP and PPL data scenarios. Simulation studies reveal that while MLE delivers highly efficient estimates under ideal model assumptions, its performance deteriorates in the presence of outliers or model misspecification. In contrast, MTM exhibits greater robustness and yields more stable parameter estimates across a wider range of conditions. To assess the real-world applicability of the proposed methods, we fit Weibull loss severity models to an actual insurance dataset under various truncation and censoring scenarios.

Completion Date

2026

Semester

Summer

Committee Chair

Tang, Larry

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

Statistics and Data Science

Format

PDF

Document Type

Dissertation

Language

English

STARS Citation

Alkhasha, Majed, "Learning Weibull Loss Severity Models From Truncated And Censored Data" (2026). Graduate Studies Theses and Dissertations 2026. 226.
https://stars.library.ucf.edu/gradstudies_etd_2026/226