ABSTRACT

Extreme value theory (EVT) deals with extreme (rare) events, which are sometimes reported as outliers. Certain textbooks encourage readers to remove outliers-in other words, to correct reality if it does not fit the model. Recognizing that any model is only an approximation of reality, statisticians are eager to extract information about unknown di

part |2 pages

Part I: Distribution of Extremes

chapter 1|18 pages

Methods of Extreme Value Theory

chapter 2|20 pages

Maximum of Partial Sums

chapter 3|24 pages

Extremes in Samples of Random Size

chapter 4|26 pages

Poisson Approximation

chapter 5|10 pages

Compound Poisson Approximation

chapter 6|20 pages

Exceedances of Several Levels

chapter 7|10 pages

Processes of Exceedances

chapter 8|10 pages

Beyond Compound Poisson

part |2 pages

Part II: Statistics of Extremes

chapter 9|48 pages

Inference on Heavy Tails

chapter 10|34 pages

Value-at-Risk

chapter 11|12 pages

Extremal Index

chapter 12|36 pages

Normal Approximation

chapter 13|30 pages

Lower Bounds

chapter 14|48 pages

Appendix