In the era of Big Data, modeling asymmetric processes requires a departure from traditional symmetric loss functions to achieve reliable Bayesian inference. This paper addresses the challenge of estimating parameters for large-scale lognormal distributions by introducing a suite of advanced loss functions. We systematically analyze the impact of Generalized Entropy, Generalized Linex, Logarithmic Squared Error, and Weighted Linex loss functions on the efficiency of Bayesian estimators. Unlike standard approaches, these functions are specifically engineered to handle the skewedness and scale of massive datasets by providing a more nuanced penalty structure. Our comparative analysis reveals that the integration of generalized and weighted loss functions significantly enhances the stability and accuracy of posterior estimates in large-volume, asymmetric data environments. The findings provide critical insights for developing robust predictive models in fields where lognormal-distributed data are prevalent, such as finance, reliability engineering, and bioinformatics.
Goodarzi, F., Behzadi, M. H. & Rostamy Malkhalifeh, M. (2026). Advanced Bayesian Inference for Big Data of Lognormal Distribution under Generalized, logarithmic and weighted Loss Function. International Journal of Nonlinear Analysis and Applications, (), 1–9. https://doi.org/10.22075/ijnaa.2026.41417.5707
MLA
Goodarzi, F., Behzadi, M. H., & Rostamy Malkhalifeh, M. "Advanced Bayesian Inference for Big Data of Lognormal Distribution under Generalized, logarithmic and weighted Loss Function", International Journal of Nonlinear Analysis and Applications, , 2026, 1–9. doi: 10.22075/ijnaa.2026.41417.5707
HARVARD
Goodarzi, F., Behzadi, M. H., & Rostamy Malkhalifeh, M. (2026). 'Advanced Bayesian Inference for Big Data of Lognormal Distribution under Generalized, logarithmic and weighted Loss Function', International Journal of Nonlinear Analysis and Applications, (), pp. 1–9. doi: 10.22075/ijnaa.2026.41417.5707
CHICAGO
Goodarzi, F., Behzadi, M. H. & Rostamy Malkhalifeh, M., "Advanced Bayesian Inference for Big Data of Lognormal Distribution under Generalized, logarithmic and weighted Loss Function." International Journal of Nonlinear Analysis and Applications, (2026): 1–9, doi: 10.22075/ijnaa.2026.41417.5707
VANCOUVER
Goodarzi F., Behzadi M. H., Rostamy Malkhalifeh M. Advanced Bayesian Inference for Big Data of Lognormal Distribution under Generalized, logarithmic and weighted Loss Function. IJNAA. 2026;():1–9. doi: 10.22075/ijnaa.2026.41417.5707
International Journal of Nonlinear Analysis and Applications