Alpha Power Type II-G Family: Adding a Power Parameter of Distributions
Bibliographic record
Abstract
This paper introduces a new family of distributions named the Alpha Power Type II-G (APII-G) family, which emerges as a groundbreaking modeling strategy for examining data governed by univariate continuous distributions.This family aims to enhance the modeling capabilities of continuous prior distributions to better fit the data utilizing a new function encompassing the additional parameter power.The innovative methodology implemented encompasses two continuous distributions: firstly, the oneparameter exponential distribution, which engendered a fresh two-parameter, Alpha Power II Exponential (APIIE) distribution, and secondly, the two-parameter Weibull distribution, which yielded a new three-parameter, Alpha Power II Weibull (APIIW) distribution.Moreover, a scrutiny of the characteristics and statistical functions, and the estimations of the parameters of the two distributions.The efficacy of these estimators is substantiated through simulation studies and finding the mean square error (MSE) and bias values of the estimators compared to sample sizes.It has been empirically proven that the two suggested models outperformed the asymptotic distributions they were compared against using multiple goodness-fit criteria as Akaike information criterion (AIC), Bayesian information criterion (BIC), corrected AIC (CAIC) and Hannan-Quinn information criterion (HQIC) on authentic datasets, The values of these criteria appeared to be the lowest for the two new distributions, which means that the new distributions are the best, especially in the context of the given data.
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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 | 0.016 | 0.053 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".