A New Family of Generalized Distributions, with Applications and Benchmarking against Machine Learning Models

Bassant  Elkalzah; Emmanuel E.  Oguadimma; Victory C.  Obieke; Chinonso Michael  Eze; Okechukwu J.  Obulezi; Mohammed  Elgarhy

doi:10.6000/1929-6029.2025.14.80

Authors

Bassant Elkalzah Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11432, Saudi Arabia and Department of Statistics, Mathematics and Insurance, Faculty of Business, Alexandria University, Alexandria, 21526, Egypt
Emmanuel E. Oguadimma Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA
Victory C. Obieke Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA
Chinonso Michael Eze Department of Statistics, Faculty of Physical Sciences, University of Nigeria, Nsukka, Nigeria
Okechukwu J. Obulezi Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, P.O. Box 5025 Awka, Nigeria
Mohammed Elgarhy Faculty of Computers and Information Systems, Egyptian Chinese University, Nasr City, Egypt; Department of Basic Sciences, Higher Institute of Administrative Sciences, Belbeis, AlSharkia, Egypt and Department of Computer Engineering, Biruni University, 34010, Istanbul, Turkey

DOI:

https://doi.org/10.6000/1929-6029.2025.14.80

Keywords:

Generalized distributions, Lomax tangent generalized family, Monte Carlo Simulation, Log-Gaussian Mixture Model, Masked Autoregressive Flow

Abstract

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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