The Shapiro–Wilk test (SW) and the Anderson–Darling test (AD) turned out to be strong procedures for testing for normality. They are joined by a class of tests for normality proposed by Epps and Pulley that, in contrast to SW and AD, have been extended by Baringhaus and Henze to yield easy-to-use affine invariant and universally consistent tests for normality in any dimension. The limit null distribution of the Epps–Pulley test involves a sequences of eigenvalues of a certain integral operator induced by the covariance kernel of a Gaussian process. We solve the associated integral equation and present the corresponding eigenvalues.

夏皮罗-威尔克检验 (SW) 和安德森-达林检验 (AD) 被证明是检验正态性的有力程序。与 Epps 和 Pulley 提出的一类正态性检验相结合，与 SW 和 AD 相比，Baringhaus 和 Henze 已对其进行了扩展，以产生易于使用的仿射不变量和普遍一致的任何维度正态性检验。Epps-Pulley 检验的极限零分布涉及由高斯过程的协方差核引起的某个积分算子的特征值序列。我们求解相关的积分方程并给出相应的特征值。