Bibliographic record
Abstract
Discrete data often exhibit variation greater or smaller than predicted by a simple model. Negative binomial distribution and beta-binomial distribution are popular and widely used to accommodate the extra-Poisson and extra-binomial variations respectively in analyzing discrete data. Weibull distribution is one of the most popular distributions in survival data analysis. Often both discrete and survival data appear in groups and it may be of interest to compare certain characteristics of two groups of such data. The purpose of this dissertation is to deal with Behrens-Fisher analogs for data that follow negative binomial, beta-binomial and Weibull distributions. We first develop six test procedures, namely, LR, LR ( bc ), T 2 , T 2 ( bc ), T 1 and T N , for testing the equality of two negative binomial means assuming unequal dispersion parameters. A simulation study is conducted to compare the performance of the test procedures. Two sets of data are analyzed. For small to moderate sample sizes, the statistic T 1 shows best overall performance. For large sample sizes, all six statistics perform well and are found similar in terms of maintaining size and power. We, then, develop eight test procedures, namely, LR, C ml , C kmm , C qb , C qs , C eq , C rs and C ars , for testing the equality of proportions in two beta-binomial distributions where the dispersion parameters are assumed unknown and unequal. These test procedures are compared through simulation studies and data analysis. The LR test is observed to maintain the nominal level reasonably well accompanied with the best power performance. The next best is the performance of the statistic C eq in terms of nominal level and power. Last but not least, we develop four test procedures, namely, LR, C ml , C cr and C tg , for testing the equality of scale parameters of two Weibull distributions where the shape parameters are unequal and compare these statistics through simulation studies and data analysis. For small sample sizes, the statistics LR and C ml hold nominal level most effectively. The statistic C cr shows highest power although its level is also higher (liberal). For moderate and large sample sizes the overall performance of the statistic LR is found to be superior to others.
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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 | 0.001 |
| 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 | 0.000 |
| 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".