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修订与更正：二维列联表中 Pearson 卡方统计量的矩与最小期望值
T. Lewis, I. W. Saunders, M. Westcott, Amendments and Corrections: The Moments of the Pearson Chi-Squared Statistic and the Minimum Expected Value in Two-Way Tables, Biometrika, Vol. 76, No. 2 (Jun., 1989), p. 407
关于二维列联表 Pearson 卡方统计量矩与最小期望频数的更正说明
On page 518 the expressions for u2 and v2 should be In view of the complexity of the formula (3·1), it is worth noting that it gives the same numerical results, in a number of examples, as the subsequent formula of Mielke & Berry (1985). It also agrees numerically in these examples with the exact third central moment calculated using the enumeration algorithm of Saunders referred to in our paper.
二维列联表中 Pearson 卡方统计量的矩与最小期望频数
Explicit expressions for the first three moments of Pearson's X2 statistic for a two-way contingency table are used to investigate the accuracy of the χ2 approximation to its distribution. The usual ’minimum expected value' criterion is shown to give a global bound on the accuracy of the moments, but to be too conservative. This is illustrated by examples. It is shown that the adequacy of the approximation depends on the significance level that is to be used as well as the…
Pearson 卡方统计量的矩与二维列联表的最小期望频数
Explicit expressions for the first three moments of Pearson's X2 statistic for a two-way contingency table are used to investigate the accuracy of the χ2 approximation to its distribution. The usual ’minimum expected value' criterion is shown to give a global bound on the accuracy of the moments, but to be too conservative. This is illustrated by examples. It is shown that the adequacy of the approximation depends on the significance level that is to be used as well as the…
关于无限可分点过程的一则札记
Summary In the discussion of Cliff and Ord (1975), Westcott mentioned the problem of determining those point processes which are both doubly stochastic Poisson processes and Poisson cluster processes—the dual nature is of interest in model interpretation since the underlying mechanisms are radically different. This was related to the question of which doubly stochastic Poisson processes are infinitely divisible, and it was conjectured that this occurs if and only if the…
簇点过程的存在性与混合性质
Summary Cluster point processes are defined and studied using the probability generating functional. Necessary and sufficient conditions for the existence of a cluster process are proved and applied to particular cases. A result on mixing in cluster processes is established.