Skewness-Kurtosis: small samples and power-law behavior
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913904250060800 |
|---|---|
| author | De Michele, Carlo De Bartolo, Samuele |
| author_facet | De Michele, Carlo De Bartolo, Samuele |
| contents | Skewness and kurtosis are fundamental statistical moments commonly used to quantify asymmetry and tail behavior in probability distributions. Despite their widespread application in statistical mechanics, condensed matter physics, and complex systems, important aspects of their empirical behavior remain unclear, particularly in small samples and in relation to their hypothesized power law scaling. In this work, we address both issues using a combination of empirical and synthetic data. First, we establish a lower bound for sample kurtosis as a function of sample size and skewness. Second, we examine the conditions under which the 4/3 power law relationship between kurtosis and skewness emerges, effectively extending Taylor power law to higher order moments. Our results show that this scaling behavior predominantly occurs in data sampled from heavy tailed distributions and medium, large sample sizes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16906 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Skewness-Kurtosis: small samples and power-law behavior De Michele, Carlo De Bartolo, Samuele Mathematical Physics Applications Skewness and kurtosis are fundamental statistical moments commonly used to quantify asymmetry and tail behavior in probability distributions. Despite their widespread application in statistical mechanics, condensed matter physics, and complex systems, important aspects of their empirical behavior remain unclear, particularly in small samples and in relation to their hypothesized power law scaling. In this work, we address both issues using a combination of empirical and synthetic data. First, we establish a lower bound for sample kurtosis as a function of sample size and skewness. Second, we examine the conditions under which the 4/3 power law relationship between kurtosis and skewness emerges, effectively extending Taylor power law to higher order moments. Our results show that this scaling behavior predominantly occurs in data sampled from heavy tailed distributions and medium, large sample sizes. |
| title | Skewness-Kurtosis: small samples and power-law behavior |
| topic | Mathematical Physics Applications |
| url | https://arxiv.org/abs/2506.16906 |