Probability inequalities related to Markov's theorem
Probability inequalities related to Markov's theorem
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DOI：
10.1198/000313002119
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发表时间：
2002-08-01
影响因子：
1.8
通讯作者：
Ghosh, BK
中科院分区：
文献类型：
--
作者：
Ghosh, BK
概率和统计中经常出现的一个令人感兴趣的主题是，当仅知道随机变量 X 的均值 It 和标准差 sigma 时，确定两个概率 Pr(X 大于或等于 r) 和 Pr(s < X - mu < t) 的最佳界限。本文解决了两种情况下的问题：X 是任意的以及 X 是非负的。仅使用马尔可夫定理以统一的方式提供答案。回顾了有关不平等的现有文献。给出了一些例子来说明不等式的使用。
A recurrent theme of interest in probability and statistics is to determine the best bounds for two probabilities, Pr(X greater than or equal to r) and Pr(s < X - mu < t), when only the mean It and the standard deviation sigma of a random variable X are known. This article addresses the issue under two circumstances, when X is arbitrary and when X is nonnegative. The answers are provided in a unified manner using only Markov's theorem. The existing literature on related inequalities is reviewed. Some examples are given to illustrate the use of the inequalities.