In generalized extreme value model for the r largest order statistics, denoted by rGEV, the selection of r is critical. The existing entropy difference test for selecting r is applicable to large sample. Another existing method (the score test with parametric bootstrap) is applicable to small sample, but computationally demanding. To address this problem for small sample, we propose a new method using a sequence of the goodness-of-fit tests based on the conditional cumulative distribution function (CCDF). The proposed CCDF test is easy to implement and computationally fast. The Cram{é}r-von Mises test was employed for the goodness-of-fit purpose. The proposed method is compared via Monte Carlo simulations with existing methods including the spacings, the score, and the entropy difference tests. The proposed CCDF test turned out to perform well for both small and large samples, comparable to the spacings and entropy difference tests. The utility of the proposed method is illustrated by an application to the r largest daily rainfall data in Korea. Additionally, we extended the existing methods and the CCDF test to a nonstationary rGEV model. Wide applicability of the proposed method are discussed.

翻译：在r最大次序统计量的广义极值模型（记为rGEV）中，r的选择至关重要。现有用于选择r的熵差检验适用于大样本情况。另一种现有方法（基于参数化自助法的得分检验）适用于小样本，但计算成本较高。为解决小样本下的这一问题，我们提出了一种基于条件累积分布函数（CCDF）的拟合优度检验序列新方法。所提出的CCDF检验易于实施且计算速度快。研究中采用Cramér-von Mises检验进行拟合优度评估。通过蒙特卡洛模拟，将所提方法与现有方法（包括间距检验、得分检验和熵差检验）进行比较。结果表明，所提出的CCDF检验在大小样本下均表现良好，其性能与间距检验和熵差检验相当。通过对韩国日最大降雨量r值数据的应用分析，展示了该方法的实用性。此外，我们将现有方法与CCDF检验扩展至非平稳rGEV模型，并讨论了所提方法的广泛适用性。