Parameter estimates of alpha-stable distribution and Hurst coefficients
Bibliographic record
Abstract
This paper presents a comparison of six different methods of estimating parameters for alpha-stable distributions on simulated and real data. Subsequently, the paper numerically investigates the relationship between estimated Hurst coefficients of the data used to fit alpha-stable distributions and the parameters of the distribution. Alpha-stable distributions are important since many real-life data cannot be represented by traditional distributions and the numerical investigation relating to the Hurst coefficient is motivated by the fact that many of such real-life data are rich in multifractality. The real data used for this study relate to rainfall and streamflow data, which are known to have a strong multifractal signature, and a traditional distribution usually fails to fit such data. The authors show that a connection between parameter estimates of alpha-stable distributions fitted to data rich in multifractality with their Hurst coefficient may exist. Based on the simulation study, it has been noted that out of the six parameter estimation approaches, the maximum-likelihood-based parameter estimation and the empirical-characteristic-function-based parameter estimation approaches are superior in obtaining a better estimate of the four alpha-stable parameters, which leads to reduced error in quantile estimation.
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 | 0.009 | 0.066 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| 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".