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.

众所周知，严格平稳序列的极值分布与独立且相同分布的序列的极值分布不同，因为可能发生极值聚类。在这里，我们考虑随机变量的非平稳但分布均匀的序列，该序列受适当的长期依赖限制。我们发现适当归一化的样本最大值的限制分布取决于测量序列的平均极值聚类的参数。基于这种新的表示，我们得出了连续的极端观测之间的时间的渐近分布，并构造了基于矩和似然估计的极值聚类度量。我们将结果专门化为具有周期性依赖结构的随机序列。