New Families of Generalized Lomax Distributions: Properties and Applications
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Bibliographic record
Abstract
In this paper, we propose new families of generalized Lomax distributions named T-LomaxfYg. Using the methodology of the Transformed-Transformer, known as T-X framework, the T-Lomax families introduced are arising from the quantile functions of exponential, Weibull, log-logistic, logistic, Cauchy and extreme value distributions. Various structural properties of the new families are derived including moments, modes and Shannon entropies. Several new generalized Lomax distributions are studied. The shapes of these T-LomaxfYg distributions are very flexible and can be symmetric, skewed to the right, skewed to the left, or bimodal. The method of maximum likelihood is proposed for estimating the distributions parameters and a simulation study is carried out to assess its performance. Four applications of real data sets are used to demonstrate the flexibility of T-LomaxfYg family of distributions in fitting unimodal and bimodal data sets from di erent disciplines.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 it