论文标题
泰勒的定律，用于一些人口模型的无限划分的概率分布
Taylor's Law for some infinitely divisible probabbility distributions from population models
论文作者
论文摘要
在一个随机变量的家族中，泰勒的定律或泰勒的权力定律脱落缩放是一种差异功能，可以使差异$σ^{2}> 0 $ 0 $的随机变量（rv）$ x $带来了预期$μ> 0 $作为powerof $ $ $ $ $ $ $ $：$：家庭中的RV。同等地，当$ \ logσ^{2} = a+b \logμ，\ a = \ log a $（对于某些集合中的所有RVS）时，TL会保持。在这里，我们分析了五个无限分配的两参数分布的家族中TL指数$ b $的可能值，并显示$ b $的值如何取决于这些分布的参数。这五个家族artweedie-bar-lev-enis，负二项式，复合泊松几何，复合几何散滴（或pólya-eaeppli）和伽马分布。这些家族在经验数据和人群模型中经常出现，并且它们是每种情况下我们都表现出的Markov Crocess的限制。
In a family of random variables, Taylor's law or Taylor's power law offluctuation scaling is a variance function that gives the variance $σ^{2}>0$ of a random variable (rv) $X$ with expectation $μ>0$ as a powerof $μ$: $σ^{2}=Aμ^{b}$ for finite real $A>0,\ b$ that are thesame for all rvs in the family. Equivalently, TL holds when $\log σ^{2}=a+b\log μ,\ a=\log A$, for all rvs in some set. Here we analyze thepossible values of the TL exponent $b$ in five families of infinitelydivisible two-parameter distributions and show how the values of $b$ dependon the parameters of these distributions. The five families areTweedie-Bar-Lev-Enis, negative binomial, compound Poisson-geometric,compound geometric-Poisson (or Pólya-Aeppli), and gamma distributions.These families arise frequently in empirical data and population models, and they are limit laws of Markov processes that we exhibit in each case.
