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.
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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)
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)
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)
Capéraà, P., Fougères, A.-L., Genest, C.: A non-parametric estimation procedure for bivariate extreme value copulas. Biometrika 84, 567–577 (1997)
Coles, S.G.: An Introduction to Statistical Modeling of Extreme Values. Springer, London (2001)
Coles, S., Pauli, F.: Models and inference for uncertainty in extremal dependence. Biometrika 89, 183–196 (2002)
Coles, S.G., Tawn, J.A.: Modelling extreme multivariate events. J. R. Stat. Soc. B 53, 377–392 (1991)
Coles, S.G., Heffernan, J.E., Tawn, J.A.: Dependence measures for extreme value analyses. Extremes 2, 339–365 (1999)
Cooley, D., Nychka, D.W., Naveau, P.: Bayesian spatial modeling of extreme precipitation return levels. J. Am. Stat. Assoc. 102, 824–840 (2007)
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)
de Haan, L.: A spectral representation for max-stable processes. Ann. Probab. 12, 1194–1204 (1984)
de Haan, L., Ferreira, A.: Extreme value theory: an introduction. In: Springer Series in Operations Research and Financial Engineering, 418pp. Springer, New York (2006)
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)
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)
Diebolt, J., Garrido, M., Trottier, C.: Improving extremal fit: a Bayesian regularization procedure. Reliab. Eng. Syst. Saf. 82(1), 21–31 (2003b)
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)
Dietrich, D., de Haan, L., Hüsler, J.: Testing extreme value conditions. Extremes 5, 71–85 (2002)
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)
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)
Embrechts, P., Klüppelberg, C., Mikosch, T.: Modelling Extremal Events for Insurance and Finance, 648pp. Springer, Berlin (1997)
Ferro, C.A.T., Segers, J.: Inference for clusters of extreme values. J. R. Stat. Soc. B 65, 545–556 (2003)
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)
Gilleland, E., Katz, R.W.: New software to analyze how extremes change over time. Eos 92(2), 13–14 (2011)
Heffernan, J.E.: A directory of coefficients of tail dependence. Extremes 3, 279–290 (2000)
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)
Hill, B.M.: A simple general approach to inference about the tail of a distribution. Ann. Stat. 3, 1163–1174 (1975)
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)
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)
Hosking, J.R.M., Wallis, J.R.: Regional Frequency Analysis: An Approach Based on L-Moments. Cambridge University Press, Cambridge (1997)
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)
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)
Kabluchko, Z., Schlather, M., de Haan, L.: Stationary max-stable fields associated to negative definite functions. Ann. Probab. 37(5), 2042–2065 (2009)
Kojadinovic, I., Yan, J.: Modeling multivariate distributions with continuous margins using the copula R package. Journal of Statistical Software 34, 1–20 (2010)
Ledford, A.W., Tawn, J.A.: Statistics for near independence in multivariate extreme values. Biometrika 83, 169–187 (1996)
Ledford, W.A., Tawn, J.A.: Modelling dependence within joint tail regions. J. R. Stat. Soc. B 59, 475–499 (1997)
McCulloch, J.H.: Simple consistent estimators of stable distribution parameters. Commun. Stat., Simul. Comput. 15, 1109–1136 (1986)
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
Pickands, J.: Statistical inference using extreme order statistics. Ann. Stat. 3, 119–131 (1975)
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)
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)
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)
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)
Schlather, M.: Models for stationary max-stable random fields. Extremes 5(1), 33–44 (2002)
Smith, R.L.: Maximum likelihood estimation in a class of non-regular cases. Biometrika 72, 67–90 (1985)
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)
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)
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)
van der Loo, M.P.J.: Distribution Based Outlier Detection for Univariate Data. Statistics Netherlands, The Hague (2010)
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)
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)
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)
Yee, T.W., Stephenson, A.G.: Vector generalized linear and additive extreme value models. Extremes 10, 1–19 (2007)
Yee, T.W., Wild, C.J.: Vector generalized additive models. J. R. Stat. Soc. B 58, 481–493 (1996)
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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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DOI: https://doi.org/10.1007/s10687-012-0155-0