Exploring the Lindley Distribution in Stochastic Frontier Analysis: Numerical Methods and Applications

This study introduces the Lindley Stochastic Frontier Analysis—LSFA model, a novel approach that incorporates the Lindley distribution to enhance the flexibility and accuracy of efficiency estimation. The LSFA model is compared against traditional SFA models, including the half-normal, exponential, and gamma models, using advanced numerical methods such as the Gauss–Hermite Quadrature, Monte Carlo Integration, and Simulated Maximum Likelihood Estimation for parameter estimation. Simulation studies revealed that the LSFA model outperforms in scenarios involving small sample sizes and complex, skewed distributions, particularly those characterized by gamma distributions. In contrast, traditional models such as the half-normal model perform better in larger samples and simpler settings, while the gamma model is particularly effective under exponential inefficiency distributions. Among the numerical techniques, the Gauss–Hermite Quadrature demonstrates a strong performance for half-normal distributions, the Monte Carlo Integration offers consistent results across models, and the Simulated Maximum Likelihood Estimation shows robustness in handling gamma and Lindley distributions despite higher errors in simpler cases. The application to a banking dataset assessed the performance of 12 commercial banks pre-COVID-19 and during COVID-19, demonstrating LSFA’s superior ability to handle skewed and intricate data structures. LSFA achieved the best overall reliability in terms of the root mean square error and bias, while the gamma model emerged as the most accurate for minimizing absolute and percentage errors. These results highlight LSFA’s potential for evaluating efficiency during economic shocks, such as the COVID-19 pandemic, where data patterns may deviate from standard assumptions. This study highlights the advantages of the Lindley distribution in capturing non-standard inefficiency patterns, offering a valuable alternative to simpler distributions like the exponential and half-normal models. However, the LSFA model’s increased computational complexity highlights the need for advanced numerical techniques. Future research may explore the integration of generalized Lindley distributions to enhance model adaptability with enriched numerical optimization to establish its effectiveness across diverse datasets.