Dagum Distribution: Properties and Different Methods of Estimation
Why this work is in the frame
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Bibliographic record
Abstract
This article addresses the various properties and different methods of estimation of the unknown parameters of a three-parameter Dagum distribution from the frequentist point of view. Although, our main focus is on estimation from frequentist point of view, yet, various mathematical and statistical properties of the Dagum distribution (such as quantiles, moments, moment generating function, hazard rate, mean residual lifetime, mean past lifetime, mean deviation about mean and median, various entropies, Bonferroni and Lorenz curves and order statistics) are derived. We briefly describe different frequentist approaches, namely, maximum likelihood estimators, moments estimators, L-moment estimators, percentile based estimators, least squares estimators, maximum product of spacings estimators, minimum distances estimators, Cram\'{e}r-von-Mises estimators, Anderson-Darling and right-tail Anderson-Darling estimators and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, a real data set have been analyzed for illustrative purposes.
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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 | 0.005 |
| 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