Advanced Bayesian Inference for Big Data of Lognormal Distribution under Generalized, logarithmic and weighted Loss Function

Articles in Press

Document Type : Research Paper

Authors
Faezeh Goodarzi 1
Mohammad Hassan Behzadi 1
Mohsen Rostamy Malkhalifeh 2
1 Department of Statistics, SR. C., Islamic Azad University, Tehran, Iran.
2 Department of Mathematics and Computer Science , SR.C, Islamic Azad University, Tehran, Iran.
10.22075/ijnaa.2026.41417.5707
Abstract
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.
Keywords
Bayes Inference
Lognormal Distribution
Big Data
Generalized Linex Loss Function
Logarithmic Squared Error Loss Function
Generalized Entropy Loss Function
weighted Linex Loss Function
Subjects
International Journal of Nonlinear Analysis and Applications

Articles in Press, Accepted Manuscript
Available Online from 04 October 2026

  • Receive Date 30 May 2026
  • Revise Date 06 June 2026
  • Accept Date 07 June 2026