标题： Stein 方法用于 Fréchet 近似：一种规则变化函数的方法 显示英文标题

标题： Stein's method for Fréchet approximation: a regularly varying functions approach

摘要： 我们开发了Stein的生成器比较方法的一种变体，以在实线上分布之间界定Kolmogorov、总变化和Wasserstein-1距离。我们的差异性是通过逆危险率的比值来表示的；因此，即使密度导数难以处理，它仍然易于处理。我们的主要应用涉及通过Fréchet定律对归一化极值进行近似。在这种情况下，新的差异性提供了一个定量的分布接近度度量，该度量基于底层累积分布函数在无穷处的平均正则变化。我们通过显式计算来说明这种方法，包括Pareto、Cauchy和Burr~XII分布的最大值。 显示英文摘要

摘要： We develop a variant of Stein's method of comparison of generators to bound the Kolmogorov, total variation, and Wasserstein-1 distances between distributions on the real line. Our discrepancy is expressed in terms of the ratio of reverse hazard rates; it therefore remains tractable even when density derivatives are intractable. Our main application concerns the approximation of normalized extremes by Fr\'echet laws. In this setting, the new discrepancy provides a quantitative measure of distributional proximity in terms of the average regular variation at infinity of the underlying cumulative distribution function. We illustrate the approach through explicit computations for maxima of Pareto, Cauchy, and Burr~XII distributions.