It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but identically distributed sequences of random variables subject to suitable long-range dependence restrictions. We find that the limiting distribution of appropriately normalized sample maxima depends on a parameter that measures the average extremal clustering of the sequence. Based on this new representation we derive the asymptotic distribution for the time between consecutive extreme observations and construct moment and likelihood-based estimators for measures of extremal clustering. We specialize our results to random sequences with periodic dependence structure.

翻译：众所周知,严格固定序列的极端值分布与极端集束中独立和相同分布序列的极端值分布可能不同。这里我们考虑的是非固定但相同分布的随机变量序列,但须受适当的远距离依赖性限制。我们发现,适当标准化样本最大值的有限分布取决于一个能测量该序列平均极端组合的参数。根据这一新表达式,我们得出连续极端观测与构建时刻和基于可能性的测算器之间的无症状分布,以测量极端集束措施。我们把结果专门用于随机序列,定期依赖结构。