The effective use of available information in extreme value analysis is critical because extreme values are scarce. Thus, using the $r$ largest order statistics (rLOS) instead of the block maxima is encouraged. Based on the four-parameter kappa model for the rLOS (rK4D), we introduce a new distribution for the rLOS as a special case of the rK4D. That is the generalized logistic model for rLOS (rGLO). This distribution can be useful when the generalized extreme value model for rLOS is no longer efficient to capture the variability of extreme values. Moreover, the rGLO enriches a pool of candidate distributions to determine the best model to yield accurate and robust quantile estimates. We derive a joint probability density function, the marginal and conditional distribution functions of new model. The maximum likelihood estimation, delta method, profile likelihood, order selection by the entropy difference test, cross-validated likelihood criteria, and model averaging were considered for inferences. The usefulness and practical effectiveness of the rGLO are illustrated by the Monte Carlo simulation and an application to extreme streamflow data in Bevern Stream, UK.

翻译：在极值分析中，有效利用现有信息至关重要，因为极值数据往往稀缺。因此，鼓励使用$r$阶最大次序统计量（rLOS）替代传统的块最大值方法。基于rLOS的四参数kappa模型（rK4D），我们引入了一种新的rLOS分布作为rK4D的特例，即rLOS的广义逻辑模型（rGLO）。当rLOS的广义极值模型不再能有效捕捉极值变异性时，该分布具有实用价值。此外，rGLO丰富了候选分布库，有助于确定最佳模型以产生准确且稳健的分位数估计。我们推导了新模型的联合概率密度函数、边缘分布函数和条件分布函数。在统计推断中，我们考虑了最大似然估计、Delta方法、轮廓似然、基于熵差检验的阶数选择、交叉验证似然准则以及模型平均方法。通过蒙特卡洛模拟和对英国Bevern溪流极端流量数据的应用，展示了rGLO的实用性和实际有效性。