Optimization-Based Bayesian and Robust Divergence Estimation for Continuous Parametric Models: Applications to Lifetime and Proportion Models

Makhdoom, Iman; Yaghoobzadeh Shahrastani, Shahram

doi:10.30473/coam.2026.77302.1403

Articles in Press

Document Type : Research Article

Authors

Department of Statistics, Payame Noor University, Tehran, Iran

10.30473/coam.2026.77302.1403

Abstract

Parametric modeling of continuous data plays a fundamental role in reliability analysis, survival studies, and proportion modeling. This paper develops a unified optimization-based Bayesian and robust divergence estimation framework for continuous parametric models under both censored and complete data settings. The proposed approach integrates hierarchical Bayesian and E-Bayesian inference with divergence-based robust estimation---specifically the L2E method---to enhance efficiency and stability against model misspecification and potential data contamination. For lifetime data, the framework is applied to the two-parameter Weibull distribution under progressive Type-II censoring schemes; for proportion data, it is applied to the Beta distribution under complete sampling. For the Beta distribution, the proposed E-Bayesian methodology is investigated under the simplified setting in which the second shape parameter is assumed known and fixed (ß=1). This assumption is adopted to illustrate the proposed optimization-based inferential framework while keeping the methodological development analytically tractable. Bayesian and E-Bayesian estimators are derived under both symmetric and asymmetric loss functions, including squared error, entropy, and Linex losses. The divergence-based estimator is incorporated as a robust alternative within the same optimization structure. Extensive Monte Carlo simulations are conducted to evaluate estimator performance in terms of absolute bias and mean squared error across various scenarios. Numerical illustrations further demonstrate the practical applicability of the proposed framework. The results indicate that the integrated methodology provides accurate and robust parameter estimation across different data structures, offering a flexible inferential tool for continuous parametric modeling.

Highlights

Unifies Bayesian, hierarchical Bayesian, E-Bayesian, and L2E estimation under one optimization-based framework.
Applies the framework to Weibull lifetime data under progressive Type-II censoring and to Beta proportion data.
Derives E-Bayesian estimators of the Weibull scale parameter under squared-error, LINEX, and entropy loss.
Monte Carlo simulations and a new sensitivity analysis compare bias and RMSE across all estimators.
Two real datasets, validated by Kolmogorov–Smirnov and Anderson–Darling tests, confirm practical applicability.

Keywords

Main Subjects

Simulation

References

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Optimization-Based Bayesian and Robust Divergence Estimation for Continuous Parametric Models: Applications to Lifetime and Proportion Models

References

References

Articles in Press, Accepted Manuscript Available Online from 20 August 2026

Articles in Press, Accepted Manuscript
Available Online from 20 August 2026