A New Family of Generalized Distributions, with Applications and Benchmarking against Machine Learning Models - Elkalzah, Bassant; Oguadimma, Emmanuel E.; Obieke, Victory C.; Eze, Chinonso Michael; Obulezi, Okechukwu J.; Elgarhy, Mohammed (International Journal of Statistics in Medical Research, 2025)
In this study, we introduce a new family of generalized distributions using the Lomax tangent generalized transformation. We derive the general formulas for its cumulative distribution function (CDF) and probability density function (PDF). As a specific sub-model, we construct the new generalized Lomax tangent transformed exponential (NGLTGE) distribution by using the exponential distribution as the baseline. We investigate the model’s key mathematical properties and conduct a Monte Carlo simulation, which confirms that the estimators exhibit good asymptotic behavior. A group acceptance sampling plan is also designed to demonstrate its utility in quality control. The NGLTGE model is then applied to real-world datasets from cryptocurrency, COVID-19, and breast cancer, where it consistently provides a superior statistical fit compared to related distributions. Finally, we apply the NGLTGE distribution within a machine learning framework using a PyTorch maximum likelihood estimation. The model’s predictive performance is found to be competitive with, and in some cases superior to, state-of-the-art machine learning density estimators like the Log-Gaussian Mixture Model (Log-GMM) and Masked Autoregressive Flow (MAF), especially for data with heavy tails. This work positions the NGLTGE distribution as a valuable, interpretable, and scalable model for both classic statistical and modern data science applications.