Consider the maximum of independent and identically distributed random variables. The classical result says that the renormalized sample maximum converges to an extreme value distributions, under certain conditions on the distribution function. In the present paper, we shall study the uniform rate of the convergence with respect to the Kolmogorov distance in the framework of the Stein equations. Some typical examples are raised in the paper.

中文翻译：

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通过Stein方程说明收敛到极值分布的速率

考虑独立和均匀分布的随机变量的最大值。经典结果表明，在分布函数的某些条件下，重新归一化的样本最大值收敛到极值分布。在本文中，我们将在Stein方程的框架内研究关于Kolmogorov距离的一致收敛速度。本文提出了一些典型的例子。