更改

where a and p are positive constants. This variance to mean power law is known in the physics literature as fluctuation scaling, and in the ecology literature as Taylor's law.

where a and p are positive constants. This variance to mean power law is known in the physics literature as fluctuation scaling, and in the ecology literature as Taylor's law.

Tweedie 分布是指数离散模型的一个特例，它是一类统计模型，用于描述在加性和再生卷积以及尺度变换下广义线性模式和拥有属性闭包的误差分布。这些分布包括一些常见的分布: 正态分布，泊松分佈和伽玛分布，以及更不寻常的分布，如复合泊松-伽马分布，正稳定分布和极端稳定分布。由于它们固有的尺度不变性，Tweedie 随机变量 y 证明了一个方差 var (y)到平均 e (y)幂定律: : text { var } ，(y) = a [ text { e } ，(y)] ^ p，其中 a 和 p 是正常数。这种均值幂律的变化在物理学文献中称为涨落标度，在生态学文献中称为泰勒定律。

Tweedie 分布是指数离散模型的一个特例，它是一类统计模型，用于描述在加性和再生卷积以及尺度变换下广义线性模式和拥有属性闭包的误差分布。这些分布包括一些常见的分布: 正态分布，泊松分佈和伽玛分布，以及更不寻常的分布，如复合泊松-伽马分布，正稳定分布和极端稳定分布。由于它们固有的尺度不变性，Tweedie 随机变量 y 证明了一个方差 var (y)到平均 e (y)幂定律：

 

<math>\text{var}\,(Y) = a[\text{E}\,(Y)]^p</math>，其中 a 和 p 是正常数。这种均值幂律的变化在物理学文献中称为涨落标度，在生态学文献中称为泰勒定律。

Random sequences, governed by the Tweedie distributions and evaluated by the [[Tweedie distributions|method of expanding bins]] exhibit a [[Logical biconditional|biconditional]] relationship between the variance to mean power law and power law [[autocorrelation]]s.  The [[Wiener–Khinchin theorem]] further implies that for any sequence that exhibits a variance to mean power law under these conditions will also manifest [[pink noise|''1/f'' noise]].<ref name="Kendal2011">{{cite journal |last1=Kendal |first1=W. S. |last2=Jørgensen |first2=B. |year=2011 |title=Tweedie convergence: A mathematical basis for Taylor's power law, 1/''f'' noise, and multifractality |journal=Phys. Rev. E |volume=84 |issue=6 |pages=066120 |doi=10.1103/PhysRevE.84.066120 |bibcode = 2011PhRvE..84f6120K |pmid=22304168|url=https://findresearcher.sdu.dk:8443/ws/files/55639035/e066120.pdf }}</ref>

Random sequences, governed by the Tweedie distributions and evaluated by the [[Tweedie distributions|method of expanding bins]] exhibit a [[Logical biconditional|biconditional]] relationship between the variance to mean power law and power law [[autocorrelation]]s.  The [[Wiener–Khinchin theorem]] further implies that for any sequence that exhibits a variance to mean power law under these conditions will also manifest [[pink noise|''1/f'' noise]].<ref name="Kendal2011">{{cite journal |last1=Kendal |first1=W. S. |last2=Jørgensen |first2=B. |year=2011 |title=Tweedie convergence: A mathematical basis for Taylor's power law, 1/''f'' noise, and multifractality |journal=Phys. Rev. E |volume=84 |issue=6 |pages=066120 |doi=10.1103/PhysRevE.84.066120 |bibcode = 2011PhRvE..84f6120K |pmid=22304168|url=https://findresearcher.sdu.dk:8443/ws/files/55639035/e066120.pdf }}</ref>