A modification of Silber’s algorithm to derive bounds on Gini’s concentration ratio from grouped observations
Bibliographic record
Abstract
Silber (1990) devised an algorithm to derive the bounds of Gini’s concentration ratio from grouped data, which does not require information on the limits of the income brackets, the group mean incomes, or the overall mean income. In the case of the upper bound, Silber’s algorithm entails determining the coordinates of the points of intersection of the tangents to the Lorenz Curve (LC) at the observed points, which are then used in conjunction with the G-matrix operator. In this note we derive modified coordinates of the points of intersection of the tangents to the LC at the observed points assuming that there is information on the limits of the income brackets and full or sparse information on mean incomes. We also show that if the modified coordinates are incorporated into Silber’s algorithm, the resulting estimate of the upper bound is identical to estimates of the upper bound proposed by Gastwirth, Fuller, and Ogwang.
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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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".