Mean absolute deviations for the Weibull distribution: applications in survival analysis and insurance claims

Weiqi Zhang; Zibo Wang; Eugene Pinsky

doi:https://doi.org/10.59139/stattrans-2026-013

Mean absolute deviations for the Weibull distribution: applications in survival analysis and insurance claims

Weiqi Zhang Department of Computer Science, Metropolitan College, Boston University, United States ORCID:https://orcid.org/0009-0009-2536-9529 , Zibo Wang Department of Computer Science, Metropolitan College, Boston University, United States ORCID:https://orcid.org/0009-0008-6243-3131 , Eugene Pinsky Department of Computer Science, Metropolitan College, Boston University, United States ORCID:https://orcid.org/0000-0002-3836-1851 Statistics in Transition new series, vol. 27, 2026, 2, pages: 1-14 Published online: 9 June 2026 https://doi.org/10.59139/stattrans-2026-013 Citation: Zhang W., Wang Z., Pinsky E., 2026. Mean absolute deviations for the Weibull distribution: applications in survival analysis and insurance claims. Statistics in Transition new series, 27(2), pp. 1-14. https://doi.org/10.59139/stattrans-2026-013

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ABSTRACT

The Weibull distribution is widely applied in fields such as survival analysis, reliability engineering, failure analysis, and extreme value theory. Traditionally, Maximum Likelihood Estimation (MLE) has been commonly used to estimate the parameters of this distribution. In this paper, we derive a new formula for the mean absolute deviation (MAD) about the median. We use this formula to derive a MAD-based parameter-estimation method that is computationally simpler than MLE. We apply our results to analyze the survival times of breast cancer patients and insurance claim amounts, providing evidence from biomedical and actuarial domains. We estimate parameters using MLE, MAD, and quantile-based approaches. The results show that the proposed MAD-based approach is superior to the other two methods. It demonstrates the practical application of MAD methods in survival analysis and financial risk modeling of insurance claims, where accurate modeling is crucial for understanding extreme outcomes.

KEYWORDS

Weibull

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