Discretization of the Alpha Power Weibull-G Family of Distributions: A Novel Discrete Distribution with Properties, Estimation, and Applications to Medical and Educational Data
Bibliographic record
Abstract
This article introduces a new four-parameter discrete distribution, named the discrete alpha power Weibull-exponential (DAPWE) distribution. The new distribution is obtained by applying the survival discretization method to the alpha power Weibull-G family of distributions. The new distribution is highly flexible due to its ability to exhibit symmetric and asymmetric shapes of its probability mass function. Additionally, the hazard function exhibits various shapes including uniform, increasing, decreasing, J-shaped, reversed J-shaped and bathtub showing its versatility. Furthermore, some important characteristics of the proposed distribution, such as moments, order statistics and entropy are discussed. The method of maximum likelihood approach is used to estimate the distribution’s unknown parameters. The efficiency of the maximum likelihood in estimating the model’s parameters is assessed through simulation studies. The model performance is also evaluated through four real medical and educational data sets. The results demonstrate that the suggested distribution can indeed provide a better fit to the data compared to other distributions.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".