A Leptokurtic‐Form Birnbaum‐Saunders Distribution With Applications to Finance
Bibliographic record
Abstract
ABSTRACT We propose here a new multivariate Birnbaum‐Saunders (BS‐type) distribution characterized by its leptokurtic property, making it particularly useful in the field of finance. Unlike the approach of Romeiro et al., our proposal is also based on scale mixtures of normal distributions (SMN), but with the mixing variable following a BS distribution, resulting in an asymmetric distribution. This new distribution captures leptokurtic character in the distribution, which implies heavier tails and a more pronounced peak compared to BS or StBS distributions (BS based on the Student‐t distribution), enabling more realistic modeling of financial data. The resulting multivariate BS‐type distribution is an absolutely continuous distribution whose marginal and conditional distributions have leptokurtic properties as compared to the usual univariate BS distribution. These results are a potentially necessary supplement to the recent work of Romeiro et al. This new distribution has not been discussed yet in the literature, and it enriches the family of multivariate BS distributions as it adds new features that take advantage of the presence of observations quite concentrated around the mode. By using the nice hierarchical representation, we have developed a fast and accurate EM (Expectation‐Maximization) algorithm for computing the maximum likelihood estimates, and simulation studies show its good performance, and the corresponding asymptotic properties of the estimates. Finally, we illustrate the results with a real dataset, showcasing the effectiveness and practical utility of the proposed distribution.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".