Estimation of shifted Weibull distribution parameters using continuous Hopfield neural networks: an application to investment risk modeling.

Parameter estimation is a fundamental component of statistical modeling, shaping the reliability of inferences across disciplines such as finance, engineering, and risk management. Accurate and stable estimation is particularly critical when modeling tail risks and extreme events. The Shifted Weibull Distribution (SWD) provides flexibility in reliability and financial applications; however, traditional estimation methods often struggle to balance accuracy, robustness, and computational efficiency. This study proposes a Continuous Hopfield Neural Network (CHNN)-based framework for estimating SWD parameters and compares its performance with the Newton-Raphson (NR-SWD) and Artificial Neural Network (ANN-SWD) estimators. The CHNN-SWD model is formulated through Lyapunov energy minimization to ensure stable convergence. Its performance was evaluated through simulations with varying sample sizes, using estimation accuracy, model adequacy, and computational efficiency as evaluation criteria. Empirical validation was conducted using Malaysian Shariah-compliant property investment returns (2008-2022), with risk assessment performed through Value-at-Risk (VaR), Tail Value-at-Risk (TVaR), and Kupiec backtesting. Results indicate that CHNN-SWD outperformed both NR-SWD and ANN-SWD in terms of robustness, accuracy, and stability, particularly in modeling extreme risk behavior. Overall, CHNN-SWD demonstrated superior performance across all validation criteria, establishing it as a reliable and computationally efficient estimator suitable for tail-dependent risk modeling applications.