A Flexible Extension of the Log-Logistic Distribution with Application to Cancer Data
Bibliographic record
Abstract
This article introduces the Type II Half Logistic Topp-Leone-G (TIIHLTL-G) family, which unifies the structural properties of the Type II Half Logistic-(G TIIHL-G) and Topp-Leone-G (TL-G) family of distributions. The novelty of the TIIHLTL-G family lies in its enhanced shape flexibility and ability to model various skewness and kurtosis patterns beyond those captured by existing extensions. The statistical features of the new TIIHLTL-G family have been thoroughly investigated, including the probability-weighted moment, hazard function, moments, order statistics, quantile function, and survival function. Parameters are estimated using classical techniques, with maximum likelihood estimation performing best overall. Application to two real cancer datasets demonstrates the superiority of the proposed model over competing distributions, including the Log-logistic and related variants, with lower AIC, and BIC confirming its improved goodness-of-fit and predictive accuracy.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.010 | 0.029 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".