Direct Quantile Function Estimation Using Information Principles and Its Applications in Reliability Analysis
Bibliographic record
Abstract
Jaynes's information principle, i.e., maximum entropy principle (MEP), constrained by probability weighted moments (PWM), has been well established as an alternative method to directly estimate quantile functions (QF) from samples of a random variable. The existence, unbiasedness, and efficiency of the maximum entropy QFs have been illustrated in the literature. However, the issue of how many orders of PWMs is optimal for a given sample of data remains unsolved, and applications of the maximum entropy QFs to reliability analysis in civil engineering are still obscure. This paper serves four main purposes: (1) a new general formulation is developed for the PWM-based MEP without sample normalization; (2) the optimal order of PWMs in MEP is determined by another information principle, i.e., Akaike information criterion; (3) The feasibility of the proposed maximum entropy QFs is illustrated by two case studies in probabilistic modeling of the soil undrained shear strength and the flood frequency; (4) applications of the proposed maximum entropy QFs are substantiated in QF-based first order reliability analysis of a cantilever steel beam with uncorrelated random variables and with correlated random variables. The maximum entropy QFs are compared to common empirical probability distributions, such as normal and lognormal distributions, in reliability analysis to demonstrate the advantages and disadvantages of the method developed.
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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 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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".