On stochastic orders and total positivity

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2022-09-16 DOI:10.1051/ps/2023005

L. Duembgen, Alexandre Mösching

引用次数: 0

Abstract

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.

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关于随机序和总正性

一般的随机顺序和实线上概率分布之间的似然比顺序进行了全面的评述。此外，对于随机对(X,Y)的分布，证明了当X = X时，Y的条件分布在X中相对于似然比阶递增，当且仅当(X,Y)的联合分布在一定意义上完全正于二阶(TP2)。还证明了这三类约束在弱收敛条件下是稳定的，并且TP2分布的弱收敛意味着上述条件分布的收敛。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Esaim-Probability and Statistics STATISTICS & PROBABILITY-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

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