The Asymptotic Distribution of the S–Gini Index
Bibliographic record
Abstract
Several generalizations of the classical Gini index, placing smaller or greater weights on various portions of income distribution, have been proposed by a number of authors. For purposes of statistical inference, the large sample distribution theory of the estimators of those measures of economic inequality is required. The present paper was stimulated by the use of bootstrap by Xu (2000) to estimate the variance of the estimator of the S –Gini index. It shows that the theory of L –statistics (Chernoff, Gastwirth & Johns, 1967; Shorack & Wellner, 1986) makes possible the construction of a consistent estimator for the S –Gini index and proof of its asymptotic normality. The paper also presents an explicit formula for the asymptotic variance. The formula should be helpful in planning the size of samples from which the S –Gini index can be estimated with a prescribed margin of error.
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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".