A New Odd Fréchet Lehmann Type II–G Family of Distributions: A Power Function Distribution With Theory and Applications
Bibliographic record
Abstract
Modeling complex random phenomena frequently observed in reliability engineering and medical science once thought to be an enigma. Scientists and practitioners agree that an appropriate but simple model is the best choice for this investigation. We contribute a new family referred to as an odd Fréchet Lehmann type-II (OFrLII) G family of distributions to address these issues. This new family has involved a shape parameter that modulated the tails of new models. Furthermore, we develop a list of eight new sub-models for a new family and a power function distribution (OFrLII–PF) nominated for detailed discussion. We derive several complementary mathematical properties and explicit expressions for the moments, quantile function, and order statistics. We plot possible shapes of the density and the hazard rate functions over the particular choices of the model parameters. We follow a technique known as maximum likelihood estimation to estimate unknown model parameters and a simulation study established to assess the asymptotic behavior of these MLEs. The applicability of the OFrLII–G family, is evaluated via OFrLII –PF distribution. For this, we fit two engineering and one COVID–19 pandemic dataset. Supportive results of OFrLII–PF distribution declare it as a better fit model against the well-established competitor’s ones. A modified odd Fréchet Lehmann Type II–G Family of Distributions: A Power Function Distribution with Theory and Applications
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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 | 0.017 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 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".