Some of the topics discussed here are sometimes relegated to appendices. However, since these topics must be well understood before arriving at the core of the subject, it seems sensible to discuss the preliminary topics first. The reader is advised to skim 0.1, 0.2 according to taste and background, but slow down for 0.3, which discusses the possible limiting distributions for normalized maxima of independent, identically distributed (iid) random variables. Section 0.4 treats the basic facts in the theory of regular variation and some important extensions. Regular variation is the basic analytical theory underpinning extreme value theory, and its importance cannot be overemphasized.
KeywordsMonotone Function Vary Function Uniform Convergence Auxiliary Function Real Variable
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