TENSOR NOTATION AND THE SAMPLING CUMULANTS OF k-STATISTICS*
TENSOR NOTATION AND THE SAMPLING CUMULANTS OF k-STATISTICS*
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张量表示法和 k-统计量的采样累积量*
DOI：
10.1093/biomet/39.3-4.319
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发表时间：
1952
期刊：
影响因子：
2.7
通讯作者：
E. Kaplan
中科院分区：
文献类型：
--
作者：
E. Kaplan
在文献中偶尔会发现与多变量分布有关的结果，这些多变量分布实际上独立于相应的单变量关系或花费相当大的努力从相应的单变量关系中导出，而它们实际上只是后者的非常温和的一般化，如将显示的那样。这里只讨论熟悉的n阶矩、特征函数、累积量和k统计量及其抽样累积量的概念。应该强调的是，这些概念与通常在多变量情况下使用的概念相同；唯一的新奇之处在于表示和处理它们的简明方式。
Now and then in the literature one finds results relating to multivariate distributions which are derived virtually independently of, or with considerable effort from, the corresponding univariate relations, whereas they are in fact only very mild geneializations of the latter, as will be shown. Only the familiar concepts of nmoments, characteristic functions, cumulants, and k-statistics and their sampling cumulants will be discussed here. It should be emphasized that these concepts are identical with those ordinarily used in multivariate situations; the only novelty lies in the concise manner of representing and handling them.