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A software review for extreme value analysis

Abstract

Extreme value methodology is being increasingly used by practitioners from a wide range of fields. The importance of accurately modeling extreme events has intensified, particularly in environmental science where such events can be seen as a barometer for climate change. These analyses require tools that must be simple to use, but must also implement complex statistical models and produce resulting inferences. This document presents a review of the software that is currently available to scientists for the statistical modeling of extreme events. We discuss all software known to the authors, both proprietary and open source, targeting different data types and application areas. It is our intention that this article will simplify the process of understanding the available software, and will help promote the methodology to an expansive set of scientific disciplines.

References

  • Apputhurai, P., Stephenson, A.G.: Accounting for uncertainty in extremal dependence modeling using Bayesian model averaging techniques. J. Stat. Plan. Inference 141, 1800–1807 (2011)

    MathSciNet  MATH  Article  Google Scholar 

  • Asquith, W.H.: lmomco: L-moments, Trimmed L-moments, L-comoments, and Many Distributions. R package version 0.97.4 ed. (2009)

  • Beirlant, J., Goegebeur, Y., Segers, J., Teugels, J.: Statistics of Extremes. Wiley, Chichester (2004)

    MATH  Book  Google Scholar 

  • Brodtkorb, P., Johannesson, P., Lindgren, G., Rychlik, I., Rydén, J., Sjö, E., WAFO—a Matlab toolbox for the analysis of random waves and loads. In: Proc. 10’th Int. Offshore and Polar Eng. Conf., vol. 3. ISOPE, Seattle, USA (2000)

    Google Scholar 

  • Capéraà, P., Fougères, A.-L., Genest, C.: A non-parametric estimation procedure for bivariate extreme value copulas. Biometrika 84, 567–577 (1997)

    MathSciNet  MATH  Article  Google Scholar 

  • Coles, S.G.: An Introduction to Statistical Modeling of Extreme Values. Springer, London (2001)

    MATH  Google Scholar 

  • Coles, S., Pauli, F.: Models and inference for uncertainty in extremal dependence. Biometrika 89, 183–196 (2002)

    MathSciNet  MATH  Article  Google Scholar 

  • Coles, S.G., Tawn, J.A.: Modelling extreme multivariate events. J. R. Stat. Soc. B 53, 377–392 (1991)

    MathSciNet  MATH  Google Scholar 

  • Coles, S.G., Heffernan, J.E., Tawn, J.A.: Dependence measures for extreme value analyses. Extremes 2, 339–365 (1999)

    MATH  Article  Google Scholar 

  • Cooley, D., Nychka, D.W., Naveau, P.: Bayesian spatial modeling of extreme precipitation return levels. J. Am. Stat. Assoc. 102, 824–840 (2007)

    MathSciNet  MATH  Article  Google Scholar 

  • Dalrymple, T.: Flood frequency analyses. Water Supply Paper 1543-A, U.S. Geological Survey, Reston, VA (1960)

  • Davison, A.C., Padoan, S.A., Ribatet, M.: Statistical modelling of spatial extremes. Stat. Sci. 27(2), 161–186 (2012)

    MathSciNet  Article  Google Scholar 

  • de Haan, L.: A spectral representation for max-stable processes. Ann. Probab. 12, 1194–1204 (1984)

    MathSciNet  MATH  Article  Google Scholar 

  • de Haan, L., Ferreira, A.: Extreme value theory: an introduction. In: Springer Series in Operations Research and Financial Engineering, 418pp. Springer, New York (2006)

    Google Scholar 

  • Dekkers, A.L.M., Einmahl, J.H.J., de Haan, L.: A moment estimator for the index of an extreme-value distribution. Ann. Stat. 17, 1833–1855 (1989)

    MATH  Article  Google Scholar 

  • Diebolt, J., Ecarnot, J., Garrido, M., Girard, S., Lagrange, D.: Le logiciel Extremes, un outil pour l’étude des queues de distribution. Revue Modulad 30, 53–60 (2003a)

    Google Scholar 

  • Diebolt, J., Garrido, M., Trottier, C.: Improving extremal fit: a Bayesian regularization procedure. Reliab. Eng. Syst. Saf. 82(1), 21–31 (2003b)

    Article  Google Scholar 

  • Diebolt, J., Garrido, M., Girard, S.: A goodness-of-fit test for the distribution tail. In: Ahsanulah, M., Kirmani, S. (eds.) Extreme Value Distributions, pp. 95–109. Nova Science, New York (2007)

    Google Scholar 

  • Dietrich, D., de Haan, L., Hüsler, J.: Testing extreme value conditions. Extremes 5, 71–85 (2002)

    MathSciNet  Article  Google Scholar 

  • Drees, H., de Haan, L., Li, D.: Approximations to the tail empirical distribution function with application to testing extreme value conditions. J. Stat. Plan. Inference 136, 3498–3538 (2006)

    MATH  Article  Google Scholar 

  • El Adlouni, S., Bobée, B., Ouarda, T.B.M.J.: On the tails of extreme event distributions in hydrology. J. Hydrol. 355, 16–33 (2008)

    Article  Google Scholar 

  • Embrechts, P., Klüppelberg, C., Mikosch, T.: Modelling Extremal Events for Insurance and Finance, 648pp. Springer, Berlin (1997)

    MATH  Book  Google Scholar 

  • Ferro, C.A.T., Segers, J.: Inference for clusters of extreme values. J. R. Stat. Soc. B 65, 545–556 (2003)

    MathSciNet  MATH  Article  Google Scholar 

  • Gençay, R., Selçuk, F., Ulugülyaǧci, A.: EVIM: a software package for extreme value analysis in MATLAB. Stud. Nonlinear Dyn. Econom. 5(3), 213–239 (2001)

    Article  Google Scholar 

  • Gilleland, E., Katz, R.W.: New software to analyze how extremes change over time. Eos 92(2), 13–14 (2011)

    Article  Google Scholar 

  • Heffernan, J.E.: A directory of coefficients of tail dependence. Extremes 3, 279–290 (2000)

    MathSciNet  MATH  Article  Google Scholar 

  • Heffernan, J.E., Tawn, J.A.: A conditional approach for multivariate extreme values (with discussion). J. R. Stat. Soc., Ser. B 66, 497–546 (2004)

    MathSciNet  MATH  Article  Google Scholar 

  • Hill, B.M.: A simple general approach to inference about the tail of a distribution. Ann. Stat. 3, 1163–1174 (1975)

    MATH  Article  Google Scholar 

  • Hosking, J.R.M.: L-moments: analysis and estimation of distributions using linear combinations of order statistics. J. R. Stat. Soc., Ser. B 52, 105–124 (1990)

    MathSciNet  MATH  Google Scholar 

  • Hosking, J.R.M.: L-moments, R package version 1.5 ed. (2009a)

  • Hosking, J.R.M.: Regional frequency analysis using L-moments, R package version 2.2 ed. (2009b)

  • Hosking, J.R.M., Wallis, J.R.: Parameter and quantile estimation for the Generalized Pareto distribution. Technometrics 29(3), 339–349 (1987)

    MathSciNet  MATH  Article  Google Scholar 

  • Hosking, J.R.M., Wallis, J.R.: Regional Frequency Analysis: An Approach Based on L-Moments. Cambridge University Press, Cambridge (1997)

    Book  Google Scholar 

  • Hosking, J.R.M., Wallis, J.R., Wood, E.F.: Estimation of the generalized extreme-value distribution by the method of probability-weighted moments. Technometrics 27, 251–261 (1985)

    MathSciNet  Article  Google Scholar 

  • Hüsler, J., Li, D.: How to use the package TestEVC1d.r, 3pp. Available at: http://my.gl.fudan.edu.cn/teacherhome/lideyuan/research.html (2006a)

  • Hüsler, J., Li, D.: On testing extreme value conditions. Extremes 9, 69–86 (2006b)

    MathSciNet  MATH  Article  Google Scholar 

  • Kabluchko, Z., Schlather, M., de Haan, L.: Stationary max-stable fields associated to negative definite functions. Ann. Probab. 37(5), 2042–2065 (2009)

    MathSciNet  MATH  Article  Google Scholar 

  • Kojadinovic, I., Yan, J.: Modeling multivariate distributions with continuous margins using the copula R package. Journal of Statistical Software 34, 1–20 (2010)

    Google Scholar 

  • Ledford, A.W., Tawn, J.A.: Statistics for near independence in multivariate extreme values. Biometrika 83, 169–187 (1996)

    MathSciNet  MATH  Article  Google Scholar 

  • Ledford, W.A., Tawn, J.A.: Modelling dependence within joint tail regions. J. R. Stat. Soc. B 59, 475–499 (1997)

    MathSciNet  MATH  Article  Google Scholar 

  • McCulloch, J.H.: Simple consistent estimators of stable distribution parameters. Commun. Stat., Simul. Comput. 15, 1109–1136 (1986)

    MathSciNet  MATH  Article  Google Scholar 

  • McNeil, A., Stephenson, A.G.: evir: extreme values in R (2008)

  • Nolan, J.P.: Stable Distributions—Models for Heavy Tailed Data, 352pp. Birkhauser, Boston (2007). ISBN-13: 9780817641597

  • Oesting, J., Kabluchko, Z., Schlather, M.: Simulation of Brown–Resnick processes. Extremes 15(1), 89–107 (2012). doi:10.1007/s10687-011-0128-8

    MathSciNet  Article  Google Scholar 

  • Pickands, J.: Statistical inference using extreme order statistics. Ann. Stat. 3, 119–131 (1975)

    MathSciNet  MATH  Article  Google Scholar 

  • Pickands, J.: Multivariate extreme value distributions. In: Proc. 43rd Sess. Int. Statist. Inst., vol. 49, pp. 859–878 (1981)

  • R Development Core Team: R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria (2012). ISBN 3-900051-07-0

  • Reiss, R.D., Thomas, M.: Statistical Analysis of Extreme Values, From Insurance, Finance Hydrology and Other Fields. Birkhauser, New York (2001)

    MATH  Google Scholar 

  • Reiss, R.D., Thomas, M.: Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields, 3rd edn. Birkhauser, New York (2007)

    MATH  Google Scholar 

  • Ribatet, M.: POT: Generalized Pareto Distribution and Peaks Over Threshold, R package verions 1.1-0 ed. (2009)

  • Ribatet, M.: SpatialExtremes: Modelling Spatial Extremes, R package version 1.8-5 (2011)

  • Rootzén, H., Tajvidi, N.: Multivariate generalized Pareto distributions. Bernoulli 12(5), 917–930 (2006)

    MathSciNet  MATH  Article  Google Scholar 

  • Rue, H., Martino, S., Chopin, N.: Approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations (with discussion). J. R. Stat. Soc. B 71, 319–392 (2009)

    MathSciNet  MATH  Article  Google Scholar 

  • Schlather, M.: Models for stationary max-stable random fields. Extremes 5(1), 33–44 (2002)

    MathSciNet  MATH  Article  Google Scholar 

  • Smith, R.L.: Maximum likelihood estimation in a class of non-regular cases. Biometrika 72, 67–90 (1985)

    MathSciNet  MATH  Article  Google Scholar 

  • Smith, R.L.: Max-stable processes and spatial extreme. http://www.stat.unc.edu/postscript/rs/spatex.pdf (1990)

  • Southworth, H.: ismev: An Introduction to Statistical Modeling of Extreme Values, Original S functions written by Janet E. Heffernan, S-PLUS pacakge by Harry Southworth. S-PLUS package version 1.2 ed. (2007)

  • Southworth, H., Heffernan, J.E.: texmex: Threshold exceedences and multivariate extremes, R package version 1.0 (2010)

  • Stephenson, A.G.: evd: extreme value distributions. R News 2(2), 31–32 (2002)

    Google Scholar 

  • Stephenson, A.G.: ismev: An Introduction to Statistical Modeling of Extreme Values, Original S functions written by Janet E. Heffernan with R port and documentation provided by A. G. Stephenson. R package version 1.35 ed. (2011)

  • Stephenson, A.G., Gilleland, E.: Software for the analysis of extreme events: the current state and future directions. Extremes 8, 87–109 (2005)

    MathSciNet  MATH  Article  Google Scholar 

  • Stephenson, A.G., Ribatet, M.: evdbayes: Bayesian analysis in extreme value theory, R package version 1.0-8 ed. (2010)

  • Stephenson, A.G., Tawn, J.A.: Bayesian inference for extremes: accounting for the three extremal types. Extremes 7, 291–307 (2004)

    MathSciNet  MATH  Article  Google Scholar 

  • van der Loo, M.P.J.: Distribution Based Outlier Detection for Univariate Data. Statistics Netherlands, The Hague (2010)

    Google Scholar 

  • Wallis, J.R.: Risk and uncertainties in the evaluation of flood events for the design of hydraulic structures. In: Guggino, E., Rossi, G., Todini, E. (eds.) Piene e Siccità, pp. 3–36. Fondazione Politecnica del Mediterraneo, Catania (1980)

    Google Scholar 

  • Wong, T.S.T., Li, W.K.: A note on the estimation of extreme value distributions using maximum product of spacings. IMS Lecture Notes 52, 272–283 (2006)

    MathSciNet  Google Scholar 

  • Wuertz, D.: fExtremes: Rmetrics—Extreme Financial Market Data, R package version 2100.77 ed. (2009)

  • Yee, T.W.: The VGAM package for categorical data analysis. Journal of Statistical Software 32, 1–34 (2010)

    MathSciNet  Google Scholar 

  • Yee, T.W., Stephenson, A.G.: Vector generalized linear and additive extreme value models. Extremes 10, 1–19 (2007)

    MathSciNet  MATH  Article  Google Scholar 

  • Yee, T.W., Wild, C.J.: Vector generalized additive models. J. R. Stat. Soc. B 58, 481–493 (1996)

    MathSciNet  MATH  Google Scholar 

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Correspondence to Eric Gilleland.

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Gilleland, E., Ribatet, M. & Stephenson, A.G. A software review for extreme value analysis. Extremes 16, 103–119 (2013). https://doi.org/10.1007/s10687-012-0155-0

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Keywords

  • Extreme value theory
  • Software development
  • Spatial extremes
  • Statistical computing