Robust Quasi-Bayesian Estimation of the Total Time on Test Transform for the Classical Pareto Distribution

The classical Pareto distribution is a foundational model for the heavy-tailed phenomena, particularly in reliability analysis, where the Total Time on Test (TTT) transform serves as a key measure. However, conventional estimation techniques for the TTT transform, such as those based on Maximum Likelihood, are sample-sensitive and biased, especially in small samples, which are common challenges with heavy-tailed data. To address these limitations, the present study proposes a robust estimation framework based on Quasi-Bayesian methodology. The estimators are derived under both Gamma and Jeffrey’s priors, and with symmetric Squared Error and asymmetric loss functions to accommodate diverse inferential objectives. To further enhance estimator stability and mitigate overfitting, the shrinkagebased technique and penalization via L1 (Lasso-type) and L2 (Quadratic) are introduced. The performance of these novel estimators is systematically evaluated against classical methods and Thompson-type shrinkage estimators via a comprehensive Monte Carlo simulation study. The results demonstrate the superior finite-sample properties, in terms of bias and Mean Squared Error(MSE), of the proposed regularized and shrinkage estimators, particularly in small-sample settings. An application to a real-world insurance claims dataset illustrates the practical implications and utility of our proposed methodologies for risk assessment.