A New Alternative to the Log-Kumaraswamy Distribution: Properties, Estimation, and Fitting Data
Bibliographic record
Abstract
Statistical distributions play a crucial role in modelling real-life data in various fields. Recently, various statistical distributions have been proposed and used in real-life data analysis. This paper introduces a novel statistical distribution as an alternative to the log-Kumaraswamy distribution. It is called the power log-Kumaraswamy distribution. We explore several distributional properties of the suggested distribution. We consider nine estimation techniques, namely, maximum likelihood, Cramér-von Mises, maximum product of spacing, least squares, weighted least squares, Anderson–Darling, right-tailed Anderson–Darling, minimum spacing absolute distance, and minimum spacing absolute-log distance methods to estimate the parameters of the introduced distribution. The performances of these estimators are evaluated via an extensive Monte Carlo simulation study. Furthermore, the applicability and superiority of the power log-Kumaraswamy distribution are demonstrated through two practical data examples from engineering and health economics. The goodness-of-fit analysis’s results support the proposed distribution’s superiority over its main competitors.
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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".