On a Transmuted Distribution Based on Log-Logistic and Ailamujia Hazard Functions with Application to Lifetime Data
Bibliographic record
Abstract
Abstract In the past few decades, numerous distributions have been proposed in the literature to model lifetime data. In this paper, the two popular distributions, Log-Logistic and Ailamujia, were selected and combined to create a new distribution, namely the Log-Logistic Ailamujia distribution, to obtain a distribution that is flexible to fit data. First, its probability density and cumulative distribution functions are presented. Then, some distributional properties such as survival function, hazard function, weighted moments, order statistics, and entropy are investigated. Next, the parameters are estimated by the maximum likelihood method, and their performance is evaluated via a simulation study with varying parameter values and sample sizes. Finally, the proposed distribution is fitted to a real-life data set to examine its flexibility. The results indicate that the new distribution performs well. Furthermore, based on the three information criteria, the proposed distribution provides a more appropriate model than other candidate distributions in terms of goodness of fit.
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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 | 0.010 | 0.028 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".