Higher order asymptotic expansions for the distribution of the sample correlation coefficient
Higher order asymptotic expansions for the distribution of the sample correlation coefficient
复制标题
样本相关系数分布的高阶渐近展开式
DOI：
10.1080/03610918408812366
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发表时间：
1984
期刊：
影响因子：
--
通讯作者：
S. Konishi
中科院分区：
文献类型：
--
作者：
N. Niki;S. Konishi
对于正态样本中的样本相关系数r的分布，得到高阶渐近展开式。所得公式保证精确到小数点后五位，并且可以被视为即使在样本量小至 11 时也能生成 r 概率积分的精确值的表达式。还给出了 r 分布百分位数的 Cornish-Fisher 逆展开式。在该结果的特定情况下，获得 r 分布中值的渐近展开，与 Kraemer (1973) 的 t 近似相关。
A higher order asymptotic expansion is obtained for the distribution of the sample correlation coefficient r in a normal sample. The resulting formula guarantees accuracy to five decimal places and may be regarded as an expression which generates exact values of the probability integral of r even when the sample size is as small as 11. A Cornish-Fisher inverse expansion for percentiles of the distribution of r is also given. In a particular case of this result, an asymptotic expansion for the median of the distribution of r is obtained, related to a t-approximation due to Kraemer (1973).