Comparison of Probability Distribution Functions for Fitting Distillation Curves of Petroleum
Bibliographic record
Abstract
The fitting capability of 25 probability distribution functions for distillation data of petroleum fractions was analyzed in this work. Rankings of all the functions based on two different approaches were established after a statistical analysis of the fit of the functions with a data set of 137 distillation curves. In general, distribution functions with four parameters showed better fitting capability than those with three parameters. Two-parameter functions were not effective in fitting distillation data. The Weibull extreme, Kumaraswamy, and Weibull functions were found to be the best distribution functions for fitting distillation data considering their ranking and the required CPU time. These distribution functions exhibited the lowest Akaike information criterion and Bayesian information criterion average values, standard deviations lower than 1%, correlation coefficients higher than 0.999, and residuals randomly distributed without any tendency. The fitting capability of the best functions was validated with an independent set of distillation data, and the ranking was the same.
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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 | 0.012 | 0.044 |
| Meta-epidemiology (narrow) | 0.002 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.006 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".