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

Summary/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.

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