Derivation of sample oriented quantile function using maximum entropy and self‐determined probability weighted moments
Bibliographic record
Abstract
Abstract The paper proposes a new distribution free method for deriving the quantile function of a non‐negative random variable using the principle of maximum entropy (MaxEnt) subject to constraints in terms of the self‐determined probability‐weighted moments estimated from observed sample data. The principle of MaxEnt constrained by probability weighted moments (PWMs) was utilized to estimate the quantile function. For correct estimation of a quantile function, outliers must be rationally considered in the analysis. However, conventional PWM was criticized for assigning non‐exceedance probabilities to sample points based on only their rank number in an ordered series rather than the magnitude of the points themselves, hereby being unable to satisfactorily accommodate outlier in a finite sample. The difficulty in obtaining accurate PWM estimates from samples has been the main impediment to the application of the MaxEnt Principle in extreme quantile estimation. This paper is an attempt to circumvent this difficulty by the use of self‐determined probability‐weighted moments, which are completely decided by the distribution itself and sample data's magnitude. By interpreting the SD‐PWM as moment of quantile function, the paper derives a more rigorous quantile function using MaxEnt principle, which is extraordinarily suitable for cases with small samples containing outliers. An efficient algorithm is presented to estimate the unknown parameters of this sample oriented MaxEnt QF. Comparative studies and numerical analysis are performed to assess the accuracy of the proposed QF estimation method. Copyright © 2009 John Wiley & Sons, Ltd.
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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 | 0.004 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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 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".