ABSTRACT
Abstract This chapter reviews the basics of univariate extreme value analysis. The generalized extreme value (GEV) distribution is introduced as the limit distribution of sample maxima with appropriate standardization. The domains of attraction are reviewed and illustrated numerically with simulation for distributions that have different tail behaviors. Common properties of the GEV distribution are summarized. The connection to the generalized Pareto distribution is established by taking the limit of the conditional distribution over a threshold. Statistical inferences are grouped by the type of available data: the block maxima method, r largest order statistics method, the peaks-over-threshold method, and the point process method. For block maxima, the maximum product spacing method, which has been overlooked in extreme value applications, is worth highlighting for its numerical stability and competitive small sample performance in comparison with the likelihood method and the L-moments method. The efficiency gain of using r largest order statistics relative to using block maxima only is shown in a small simulation study. Compared to existing reviews on univariate extreme value analysis, this chapter provides more statistical flavor through numerical studies.
