Unit-Chen distribution and its quantile regression model with applications
Bibliographic record
Abstract
The need for new statistical distributions that can effectively fit real datasets on the unit interval is crucial in data analysis. This article introduces a new family of statistical distributions on the unit interval, called the unit-Chen distribution, derived from the two-parameter Chen distribution. The statistical properties of the proposed distribution are discussed, along with a quantile regression model based on the unit-Chen distribution. Both maximum likelihood and Bayesian procedures are used to estimate the model’s parameters. For the Bayesian approach, two methods of approximate Bayesian computation (ABC) are employed: the accept-reject (AR) method and sampling importance resampling (SIR) method. A simulation study is provided to investigate the properties of the maximum likelihood method applied. Based on well-known diagnostic tests, the simulation data presented in this paper is appropriate. To demonstrate the applicability of the proposed models, real-life datasets (four using unit-Chen and one using unit-Chen regression) are analyzed. The performance of the proposed models is compared with other well-known distributions. The comparison results indicate that the unit-Chen and unit-Chen regression models fit the data better than the competitive models applied in this study.
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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 | 0.007 | 0.025 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| 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 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".