论文标题
在随机订单和总阳性上
On Stochastic Orders and Total Positivity
论文作者
论文摘要
在真实线上的概率分布之间进行了通常的随机顺序和似然比顺序，以完全一般性进行审查。此外，对于随机对$（x，y）$的分布，证明$ y $（给定$ x = x $）的条件分布在$ x = x $方面的可能性比顺序在$ x $上增加，并且仅当$（x，y）$的联合分布完全是$（x，y）$完全是二（x，y）的订单二（x，y）。还表明，这三种类型的约束在弱收敛下是稳定的，而TP2分布的弱收敛性意味着刚刚提到的条件分布的收敛性。
The usual stochastic order and the likelihood ratio order between probability distributions on the real line are reviewed in full generality. In addition, for the distribution of a random pair $(X,Y)$, it is shown that the conditional distributions of $Y$, given $X = x$, are increasing in $x$ with respect to the likelihood ratio order if and only if the joint distribution of $(X,Y)$ is totally positive of order two (TP2) in a certain sense. It is also shown that these three types of constraints are stable under weak convergence, and that weak convergence of TP2 distributions implies convergence of the conditional distributions just mentioned.
