極端值建模和估算是各種應(yīng)用領(lǐng)域的重要挑戰(zhàn)，例如環(huán)境溢陪，水文萍虽，金融，精算科學(xué)形真。
樣本的極端部分可能非常重要杉编。也就是說，它可能表現(xiàn)出更大的潛在風(fēng)險咆霜，例如高濃度的空氣污染物邓馒，洪水，極端索賠規(guī)模蛾坯。
一般而言光酣，極端之建模有三個方面：
Univariate Extreme Value Theory:
單變量極值理論。Bivariate Extreme Value Theory:
雙變量極值理論
- Multivariate Extreme Value Theory:
多變量極值理論
與極值相關(guān)的繪圖：
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經(jīng)典的書籍以及文章
- E. Gilleland, M. Ribatet, A. Stephenson (2013). A Software Review for Extreme Value Analysis, Extremes , 16 , 103-119.
- R.-D. Reiss, M. Thomas (2007). Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields , Springer-Verlag.
- L. de Haan, A. Ferreira (2006). Extreme Value Theory: An Introduction , Springer-Verlag.
- J. Beirlant, Y. Goegebeur, J. Teugels, J. Segers (2004). Statistics of Extremes: Theory and Applications , John Wiley & Sons.
- B. Finkenstaedt, H. Rootzen (2004). Extreme Values in Finance, Telecommunications, and the Environment , Chapman & Hall/CRC.
- S. Coles (2001). An Introduction to Statistical Modeling of Extreme Values , Springer-Verlag.
- P. Embrechts, C. Klueppelberg, T. Mikosch (1997). Modelling Extremal Events for Insurance and Finance , Springer-Verlag.
- S.I. Resnick (1987). Extreme Values, Regular Variation and Point Processes , Springer-Verlag.
- Smith, R.L. (1987). Approximations in extreme value theory. Technical report 205, Center for Stochastic Process, University of North Carolina, 1–34.
- Suveges (2007) Likelihood estimation of the extremal index. Extremes, 10(1), 41-55.
- Suveges and Davison (2010), Model misspecification in peaks over threshold analysis. Annals of Applied Statistics, 4(1), 203-221.
