Do Stock Returns Adhere to the Distribution Stipulated by the Student’s T-distribution?
Bibliographic record
Abstract
When people are analyzing data with thicker tails compared to the normal distribution, student’s t-distribution is commonly applied, making it potentially relevant in the financial markets, especially returns of a stock. This research focuses on estimating the parameters of the student’s t-distribution in empirical data, employing the maximum likelihood fitting method in order to determine accurate parameters of estimation. In order to conclude whether the t-distribution is close math or not, we assess the goodness of fit, where synthetic data is generated, and the Kolmogorov-Smirnov (KS) test is applied. Moreover, to determine if the t-distribution is the best fit for the data, a Likelihood ratio test is conducted. It provides a statistical comparison between t-distribution and alternative distributions, allowing us to select the most suitable model. Furthermore, the relationship between volatility and degrees of freedom is examined using a scatterplot. This aims to uncover any potential correlation or patterns between these variables. By undertaking these investigations, we deepened our understanding of the statistical characteristics of stock returns and gained insights for potential applications in financial modeling and risk analysis.
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 | 0.027 | 0.173 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.006 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.004 |
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".