Bounded probability properties of Kolmogorov-Smirnov and similar statistics for discrete data
Bounded probability properties of Kolmogorov-Smirnov and similar statistics for discrete data
复制标题
Kolmogorov-Smirnov 的有界概率性质和离散数据的类似统计
DOI：
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发表时间：
1963
期刊：
影响因子：
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通讯作者：
J. Walsh
中科院分区：
文献类型：
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作者：
J. Walsh
摘要考虑了一类比较一般的情形，包括Kolmogorov-Smirnov型结果作为特例。当使用的样本值来自任何性质的连续总体时，这些情况都要求具有唯一确定的概率属性，这些情况将在以下各节中描述。然而，如果抽样的总体是离散的，则这些概率值不是唯一确定的。本文证明了连续情况下的值表示在任何离散情况下出现的值的界。用于显示这些约束关系成立的方法在于注意到任何离散数据情况都可以被解释为涉及连续数据分组的情况。然后，在分组数据情况的概率值与相应的未分组数据情况之间建立绑定关系，所述未分组数据情况是针对连续数据的情况而考虑的情况。这些关于离散数据情况的概率界在实际应用中应该是有用的。实际上，所有数据都是离散的(由于测量精度的限制)。
SummaryA somewhat general class of situations, that include Kolmogorov-Smirnov type results as special cases, is considered. These situations, which are described in the following sections, are required to have uniquely determined probability properties when the sample values used are from continuous populations of any nature. If the populations sampled are discrete, however, these probability values are not uniquely determined. This paper shows that the values for the continuous case represent bounds for the values that occur in any discrete case. The method used to show that these bound relations hold consists in noting that any discrete data situation can be interpreted as a situation involving the grouping of continuous data. Then bound relationships are established between the values of probabilities for the grouped data situations and the corresponding ungrouped data situations, which are the situations considered for the case of the continuous data. These bounds on probabilities for discrete data cases should be useful for practical applications. In practice, all data are discrete (due to limitations in measurement accuracy).