The Topp–Leone Discrete Laplace Distribution and Its Applications
Bibliographic record
Abstract
A new Topp–Leone generated family of distributions, which we call the Topp–Leone Discrete Laplace ( $$TL-DL$$ ) distribution, is proposed. It has a shape parameter $$\alpha>0$$ and a scale parameter $$0<p<1$$ . The $$TL-DL$$ is an alternative distribution for discrete data that have an asymmetric distribution. Some mathematical properties of the proposed distribution are also derived. Namely, we present the quantile function and the moments for the $$TL-DL$$ distribution. The Maximum Likelihood procedure is applied for parameter estimation. An application study is presented using real data. We use two data sets for this part of the analysis to illustrate the applications of the $$TL-DL$$ distribution. For the first data set, the change of the stock price in comparison with the closing price for the previous day is considered. The second data set provides information about the comparison of production cycle times of employees before and after the improvement a slippery production line in the degreasing alkaline process by increasing the pressure of the nozzle. The $$TL-DL$$ distribution is applied to a real life data and it fits data more efficiently than the Discrete Laplace ( $$DL$$ ) and Discrete Normal ( $$DN$$ ) distributions.
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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 | 0.005 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".