Bonferroni-type inequalities; Chebyshev-type inequalities for the distributions on [0, n]
Bonferroni-type inequalities; Chebyshev-type inequalities for the distributions on [0, n]
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Bonferroni 型不等式；
DOI：
10.1007/bf00118635
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发表时间：
1991
期刊：
影响因子：
--
通讯作者：
M. Sibuya
中科院分区：
文献类型：
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作者：
M. Sibuya
给出了构造最严格Bonferroni型不等式的一种初等“优-劣方法”。这些基本上是集合{0，1，.上的离散概率分布的切比雪夫型不等式。n}，其中n是有关事件的个数，集合上具有特定性质的多项式导致了不等式的产生。所有已知的结果都可以很容易地用这种方法证明。进一步地，用该方法完全解决了关于所有低阶矩的不等式。作为例子，得到了最严格的三次和四次不等式。Mürgüritescu不等式的简单表达式（1987，Stud. Cerc.垫，39，246-251），改进了Galambos不等式。
An elementary “majorant-minorant method” to construct the most stringent Bonferroni-type inequalities is presented. These are essentially Chebyshev-type inequalities for discrete probability distributions on the set {0, 1,...,n}, wherenis the number of concerned events, and polynomials with specific properties on the set lead to the inequalities. All the known results are proved easily by this method. Further, the inequalities in terms of all the lower moments are completely solved by the method. As examples, the most stringent new inequalities of degrees three and four are obtained. Simpler expressions of Mărgăritescu's inequality (1987,Stud. Cerc. Mat.,39, 246–251), improving Galambos' inequality, are given.