Dispersive ordering—Some applications and examples
Dispersive ordering—Some applications and examples
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DOI：
10.1007/s00362-005-0285-4
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发表时间：
2006-03
影响因子：
1.3
通讯作者：
Jong-June Jeon;S. Kochar;C. Park
中科院分区：
文献类型：
--
作者：
Jong-June Jeon;S. Kochar;C. Park
比较概率分布之间的散布的一个基本概念是分散排序。设X和Y分别为分布函数为F和G的两个随机变量。设F − 1和G − 1是它们的右连续逆（分位数函数）。如果G −1（β）−G− 1（α）≤F−1（β）− F −1（α），对所有0<α≤β<1，我们说Y比X（Y≤dispX）分散性小。这意味着G的任何两个分位数之间的差小于F的相应分位数之间的差。Y ≤ dispX的一个推论是，|Y1−Y2|随机小于|X1−X2|而这又意味着var（Y）≤var（X）以及E [|Y1−Y2|]≤E[|X1−X2|其中X1，X2（Y1，Y2）是X（Y）的两个独立拷贝。在这篇综述文章中，我们给出了几个例子和分散序在统计中的应用。例子包括那些相关的顺序统计，间距，卷积的非同分布的随机变量和历元时间的非齐次泊松过程。
A basic concept for comparing spread among probability distributions is that of dispersive ordering. LetXandYbe two random variables with distribution functionsFandG, respectively. LetF−1andG−1be their right continuous inverses (quantile functions). We say thatYis lessdispersedthanX(Y≤dispX) ifG−1(β)−G−1(α)≤F−1(β)−F−1(α), for all 0<α≤β<1. This means that the difference between any two quantiles ofGis smaller than the difference between the corresponding quantiles ofF. A consequence ofY≤dispXis that |Y1−Y2| is stochastically smaller than |X1−X2| and this in turn impliesvar(Y)≤var(X)as well asE[|Y1−Y2|]≤E[|X1−X2|], whereX1,X2(Y1,Y2) are two independent copies ofX(Y). In this review paper, we give several examples and applications of dispersive ordering in statistics. Examples include those related to order statistics, spacings, convolution of non-identically distributed random variables and epoch times of non-homogeneous Poisson processes.