A New Family of Generalized Distributions, with Applications and Benchmarking against Machine Learning Models
DOI:
https://doi.org/10.6000/Keywords:
Generalized distributions, Lomax tangent generalized family, Monte Carlo Simulation, Log-Gaussian Mixture Model, Masked Autoregressive FlowAbstract
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.
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