A New Family of Distributions: Libby-Novick Beta
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Bibliographic record
Abstract
We define a family of distributions, named the Libby-Novick beta family of distributions, which includes the classical beta generalized and exponentiated generators. The new family offers much more flexibility for modeling real data than these two generators and the Kumaraswamy family of distributions The extended family provides reasonable parametric fits to real data in several areas because the additional shape parameters can control the skewness and kurtosis simultaneously, vary tail weights and provide more entropy for the generated distribution. For any given distribution, we can construct a wider distribution with three additional shape parameters which has much more flexibility than the original one. The family density function is a linear combination of exponentiated densities defined from the same baseline distribution. The proposed family also has tractable mathematical properties including moments, generating function, mean deviations and order statistics. The parameters are estimated by maximum likelihood and the observed information matrix is determined. The importance of the family is very well illustrated. By means of two real data sets we demonstrate that this family can give better fits than those ones using the McDonald, beta generalized and Kumaraswamy generalized classes of distributions.
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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 | 0.003 |
| 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