A New Family of Generalized Distributions, with Applications and Benchmarking against Machine Learning Models
Bibliographic record
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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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".