Tests of exponentiality against some parametric over/under-dispersed life time models
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Bibliographic record
Abstract
We develop tests of goodness of fit of the exponential model against some over/under dispersion family of distributions. In particular, we develop 3 score test statistics and 3 likelihood ratio statistics. These are (S1, L1), (S2, L2), and (S3, L3) based on a general over-dispersed family of distributions, two specic over/under dispersed exponential models, namely, the gamma and the Weibull distributions, respectively. A simulation study shows that the statistics S3 and L3 have best overall performance, in terms of both, level and power. However, the statistic L3 can be liberal in some instances and it needs the maximum likelihood estimates of the parameters of the Weibull distribution as opposed to the statistic S3 which is very simple to use. So, our recommendation is to use the statistic S3 to test the fit of an exponential distribution over any over/under-dispersed exponential distribution.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it