Bilal-G Family of Distributions with Applications to Biomedical and Reliability Engineering Data
Bibliographic record
Abstract
This paper introduces the Bilal-G (B-G) family of distributions, a novel generator-based method for enhancing the flexibility of existing probability models to better accommodate complex data structures prevalent in biomedical and reliability engineering. Data from these fields frequently exhibit features like high skewness, significant outliers, and non-monotone hazard rates that challenge conventional distributions. Using the Bilal distribution as the generator, we construct the new family’s general cumulative distribution function (CDF) and probability density function (PDF), from which a key, parsimonious sub-model, the two-parameter Bilal-Exponential (BE) distribution, is derived. We thoroughly analyze the BE distribution’s properties, including its capability to model an increasing hazard rate, which is supported by Total Time on Test (TTT) plots of the application datasets. A comprehensive simulation study evaluates the performance of fifteen distinct non-Bayesian estimators, revealing that the Minimum Spacing Linex Distance (MSLNDE) method consistently provides the most accurate and precise parameter estimates across various sample sizes. Finally, the superiority of the BE distribution is demonstrated through its successful application to two real datasets: one on patient mortality rates and one on component failure times. For the mortality data (Data I), the BE model reduced the Akaike Information Criterion (AIC) by 1.99 units compared to the classical Weibull distribution. For the component failure data (Data II), the Bayesian Information Criterion (BIC) was reduced by 0.41 units compared to the best-fitting competing model (TIHTE), confirming the BE distribution’s exceptional goodness-of-fit and reliability as a practical lifetime model.
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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 | 0.018 | 0.059 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.005 | 0.004 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.004 | 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".