On Bias Corrected Estimators of the Two Parameter Gamma Distribution
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Bibliographic record
Abstract
The gamma distribution, which is a member of Pearson Type III family of distributions, is one of the most commonly used distribution in engineering applications since it can be used as a probability model for positive data sets exhibiting various degrees of skewness. The maximum likelihood estimators (MLE) of the two parameter gamma distribution are known to be biased, and bias-corrected estimators of the parameters are available in the literature. In this paper, we have used Monte-Carlo simulation to estimate the bias and mean squared error (MSE) of the moment estimators, the ML estimators, and bias-corrected ML estimators. Our simulations show that the bias-correction available in the literature fails to remove the bias in the MLE for small values of the shape parameter.
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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 | 0.000 | 0.007 |
| 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 it