Induced Bilal Distribution: Statistical Properties with Applications to Model Precipitation and Vinyl Chloride Data
Bibliographic record
Abstract
This paper proposes a new one parameter life distribution called induced Bilal distribution for modeling some real data. The main mathematical characteristics of this distribution are derived and discussed including the cumulative distribution and probability density functions, the moments, coefficient of variation, skewness, kurtosis, mean and median deviations, Gini index, Lorenz curve, Bonferroni curve, Rényi entropy, stochastic ordering, and distribution of order statistics. Also, reliability analysis based on the odds function, survival function, reversed hazard rate function, hazard function, and the stress-strength reliability function are provided. Estimation of the model parameter is performed using the maximum likelihood method and a simulation study is supported to illustrate the estimator behaviors. Using two real data sets related to the precipitation in Minneapolis and vinyl chloride, it is shown that the new distribution outperforms some well-known important existing competitors considered in this study.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 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".