Generalized Taylor's Law for Dependent and Heterogeneous Heavy-Tailed Data
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917003452743680 |
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| author | Cheng, Pok Him Cohen, Joel E. Ling, Hok Kan Yam, Sheung Chi Phillip |
| author_facet | Cheng, Pok Him Cohen, Joel E. Ling, Hok Kan Yam, Sheung Chi Phillip |
| contents | Taylor's law, also known as fluctuation scaling in physics and the power-law variance function in statistics, is an empirical pattern widely observed across fields including ecology, physics, finance, and epidemiology. It states that the variance of a sample scales as a power function of the mean of the sample. We study generalizations of Taylor's law in the context of heavy-tailed distributions with infinite mean and variance. We establish the probabilistic limit and analyze the associated convergence rates. Our results extend the existing literature by relaxing the i.i.d. assumption to accommodate dependence and heterogeneity among the random variables. This generalization enables application to dependent data such as time series and network-structured data. We support the theoretical developments by extensive simulations, and the practical relevance through applications to real network data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09562 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Taylor's Law for Dependent and Heterogeneous Heavy-Tailed Data Cheng, Pok Him Cohen, Joel E. Ling, Hok Kan Yam, Sheung Chi Phillip Statistics Theory Taylor's law, also known as fluctuation scaling in physics and the power-law variance function in statistics, is an empirical pattern widely observed across fields including ecology, physics, finance, and epidemiology. It states that the variance of a sample scales as a power function of the mean of the sample. We study generalizations of Taylor's law in the context of heavy-tailed distributions with infinite mean and variance. We establish the probabilistic limit and analyze the associated convergence rates. Our results extend the existing literature by relaxing the i.i.d. assumption to accommodate dependence and heterogeneity among the random variables. This generalization enables application to dependent data such as time series and network-structured data. We support the theoretical developments by extensive simulations, and the practical relevance through applications to real network data. |
| title | Generalized Taylor's Law for Dependent and Heterogeneous Heavy-Tailed Data |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2510.09562 |