1 - Introduction aux Statistiques de deuxième espèce : applications des Logs-moments et des Logs-cumulants à l'analyse des lois d'images radar
Bibliographic record
Abstract
Statistics methods classicaly used to analyse a probability density function (p.d.f.) are based on Fourier Transform, on which usefull tools as first and second characteristic functions are based, yielding the definitions of moments and cumulants. Yet this transform does not well match with p.d.f. defined on R+ as analytical expressions can be rather heavy in this case. In this article, we propose to start with a rather misknown transform: the Mellin transform, in order to define second kind statistics. By this way, second kind characteristic functions, second kind moments (log-moments) and second kind cumulants (log-cumulants) can be defined by mimicing the traditional definitions. For classical p.d.f. defined on R+, as Gamma and Nakagami laws, this approach seems to be simpler than previous one. More, for complicated p.d.f., as the famous K law or positive α-stable distributions, second kind statistics yield oversimple results. This new approach provides new methods for estimating the parameters of p.d.f. defined on R+. Comparisons can be done with traditional methods as Maximum Likehood Method and Moment Method: the variance of the new methods estimators are lower than Moment Method ones, and slightly upper than Cramer Rao bounds.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.008 | 0.005 |
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 source (direct Gemma or distilled Codex), 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".