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Extremes

, Volume 16, Issue 1, pp 103–119 | Cite as

A software review for extreme value analysis

  • Eric Gilleland
  • Mathieu Ribatet
  • Alec G. Stephenson
Open Access
Article

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.

Keywords

Extreme value theory Software development Spatial extremes Statistical computing 

References

  1. 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)MathSciNetzbMATHCrossRefGoogle Scholar
  2. Asquith, W.H.: lmomco: L-moments, Trimmed L-moments, L-comoments, and Many Distributions. R package version 0.97.4 ed. (2009)Google Scholar
  3. Beirlant, J., Goegebeur, Y., Segers, J., Teugels, J.: Statistics of Extremes. Wiley, Chichester (2004)zbMATHCrossRefGoogle Scholar
  4. 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
  5. Capéraà, P., Fougères, A.-L., Genest, C.: A non-parametric estimation procedure for bivariate extreme value copulas. Biometrika 84, 567–577 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  6. Coles, S.G.: An Introduction to Statistical Modeling of Extreme Values. Springer, London (2001)zbMATHGoogle Scholar
  7. Coles, S., Pauli, F.: Models and inference for uncertainty in extremal dependence. Biometrika 89, 183–196 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  8. Coles, S.G., Tawn, J.A.: Modelling extreme multivariate events. J. R. Stat. Soc. B 53, 377–392 (1991)MathSciNetzbMATHGoogle Scholar
  9. Coles, S.G., Heffernan, J.E., Tawn, J.A.: Dependence measures for extreme value analyses. Extremes 2, 339–365 (1999)zbMATHCrossRefGoogle Scholar
  10. Cooley, D., Nychka, D.W., Naveau, P.: Bayesian spatial modeling of extreme precipitation return levels. J. Am. Stat. Assoc. 102, 824–840 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  11. Dalrymple, T.: Flood frequency analyses. Water Supply Paper 1543-A, U.S. Geological Survey, Reston, VA (1960)Google Scholar
  12. Davison, A.C., Padoan, S.A., Ribatet, M.: Statistical modelling of spatial extremes. Stat. Sci. 27(2), 161–186 (2012)MathSciNetCrossRefGoogle Scholar
  13. de Haan, L.: A spectral representation for max-stable processes. Ann. Probab. 12, 1194–1204 (1984)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 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
  15. 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)zbMATHCrossRefGoogle Scholar
  16. 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
  17. Diebolt, J., Garrido, M., Trottier, C.: Improving extremal fit: a Bayesian regularization procedure. Reliab. Eng. Syst. Saf. 82(1), 21–31 (2003b)CrossRefGoogle Scholar
  18. 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
  19. Dietrich, D., de Haan, L., Hüsler, J.: Testing extreme value conditions. Extremes 5, 71–85 (2002)MathSciNetCrossRefGoogle Scholar
  20. 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)zbMATHCrossRefGoogle Scholar
  21. 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)CrossRefGoogle Scholar
  22. Embrechts, P., Klüppelberg, C., Mikosch, T.: Modelling Extremal Events for Insurance and Finance, 648pp. Springer, Berlin (1997)zbMATHCrossRefGoogle Scholar
  23. Ferro, C.A.T., Segers, J.: Inference for clusters of extreme values. J. R. Stat. Soc. B 65, 545–556 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 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)CrossRefGoogle Scholar
  25. Gilleland, E., Katz, R.W.: New software to analyze how extremes change over time. Eos 92(2), 13–14 (2011)CrossRefGoogle Scholar
  26. Heffernan, J.E.: A directory of coefficients of tail dependence. Extremes 3, 279–290 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  27. 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)MathSciNetzbMATHCrossRefGoogle Scholar
  28. Hill, B.M.: A simple general approach to inference about the tail of a distribution. Ann. Stat. 3, 1163–1174 (1975)zbMATHCrossRefGoogle Scholar
  29. 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)MathSciNetzbMATHGoogle Scholar
  30. Hosking, J.R.M.: L-moments, R package version 1.5 ed. (2009a)Google Scholar
  31. Hosking, J.R.M.: Regional frequency analysis using L-moments, R package version 2.2 ed. (2009b)Google Scholar
  32. Hosking, J.R.M., Wallis, J.R.: Parameter and quantile estimation for the Generalized Pareto distribution. Technometrics 29(3), 339–349 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  33. Hosking, J.R.M., Wallis, J.R.: Regional Frequency Analysis: An Approach Based on L-Moments. Cambridge University Press, Cambridge (1997)CrossRefGoogle Scholar
  34. 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)MathSciNetCrossRefGoogle Scholar
  35. 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)
  36. Hüsler, J., Li, D.: On testing extreme value conditions. Extremes 9, 69–86 (2006b)MathSciNetzbMATHCrossRefGoogle Scholar
  37. Kabluchko, Z., Schlather, M., de Haan, L.: Stationary max-stable fields associated to negative definite functions. Ann. Probab. 37(5), 2042–2065 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  38. 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
  39. Ledford, A.W., Tawn, J.A.: Statistics for near independence in multivariate extreme values. Biometrika 83, 169–187 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  40. Ledford, W.A., Tawn, J.A.: Modelling dependence within joint tail regions. J. R. Stat. Soc. B 59, 475–499 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  41. McCulloch, J.H.: Simple consistent estimators of stable distribution parameters. Commun. Stat., Simul. Comput. 15, 1109–1136 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  42. McNeil, A., Stephenson, A.G.: evir: extreme values in R (2008)Google Scholar
  43. Nolan, J.P.: Stable Distributions—Models for Heavy Tailed Data, 352pp. Birkhauser, Boston (2007). ISBN-13: 9780817641597Google Scholar
  44. Oesting, J., Kabluchko, Z., Schlather, M.: Simulation of Brown–Resnick processes. Extremes 15(1), 89–107 (2012). doi: 10.1007/s10687-011-0128-8 MathSciNetCrossRefGoogle Scholar
  45. Pickands, J.: Statistical inference using extreme order statistics. Ann. Stat. 3, 119–131 (1975)MathSciNetzbMATHCrossRefGoogle Scholar
  46. Pickands, J.: Multivariate extreme value distributions. In: Proc. 43rd Sess. Int. Statist. Inst., vol. 49, pp. 859–878 (1981)Google Scholar
  47. R Development Core Team: R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria (2012). ISBN 3-900051-07-0Google Scholar
  48. Reiss, R.D., Thomas, M.: Statistical Analysis of Extreme Values, From Insurance, Finance Hydrology and Other Fields. Birkhauser, New York (2001)zbMATHGoogle Scholar
  49. 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)zbMATHGoogle Scholar
  50. Ribatet, M.: POT: Generalized Pareto Distribution and Peaks Over Threshold, R package verions 1.1-0 ed. (2009)Google Scholar
  51. Ribatet, M.: SpatialExtremes: Modelling Spatial Extremes, R package version 1.8-5 (2011)Google Scholar
  52. Rootzén, H., Tajvidi, N.: Multivariate generalized Pareto distributions. Bernoulli 12(5), 917–930 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  53. 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)MathSciNetzbMATHCrossRefGoogle Scholar
  54. Schlather, M.: Models for stationary max-stable random fields. Extremes 5(1), 33–44 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  55. Smith, R.L.: Maximum likelihood estimation in a class of non-regular cases. Biometrika 72, 67–90 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  56. Smith, R.L.: Max-stable processes and spatial extreme. http://www.stat.unc.edu/postscript/rs/spatex.pdf (1990)
  57. 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)Google Scholar
  58. Southworth, H., Heffernan, J.E.: texmex: Threshold exceedences and multivariate extremes, R package version 1.0 (2010)Google Scholar
  59. Stephenson, A.G.: evd: extreme value distributions. R News 2(2), 31–32 (2002)Google Scholar
  60. 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)Google Scholar
  61. Stephenson, A.G., Gilleland, E.: Software for the analysis of extreme events: the current state and future directions. Extremes 8, 87–109 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  62. Stephenson, A.G., Ribatet, M.: evdbayes: Bayesian analysis in extreme value theory, R package version 1.0-8 ed. (2010)Google Scholar
  63. Stephenson, A.G., Tawn, J.A.: Bayesian inference for extremes: accounting for the three extremal types. Extremes 7, 291–307 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  64. van der Loo, M.P.J.: Distribution Based Outlier Detection for Univariate Data. Statistics Netherlands, The Hague (2010)Google Scholar
  65. 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
  66. 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)MathSciNetGoogle Scholar
  67. Wuertz, D.: fExtremes: Rmetrics—Extreme Financial Market Data, R package version 2100.77 ed. (2009)Google Scholar
  68. Yee, T.W.: The VGAM package for categorical data analysis. Journal of Statistical Software 32, 1–34 (2010)MathSciNetGoogle Scholar
  69. Yee, T.W., Stephenson, A.G.: Vector generalized linear and additive extreme value models. Extremes 10, 1–19 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  70. Yee, T.W., Wild, C.J.: Vector generalized additive models. J. R. Stat. Soc. B 58, 481–493 (1996)MathSciNetzbMATHGoogle Scholar

Copyright information

© The Author(s) 2012

Authors and Affiliations

  • Eric Gilleland
    • 1
  • Mathieu Ribatet
    • 2
  • Alec G. Stephenson
    • 3
  1. 1.Research Applications LaboratoryNational Center for Atmospheric ResearchBoulderUSA
  2. 2.Institute of MathematicsUniversity of Montpellier IIMontpellierFrance
  3. 3.CSIRO, Mathematics, Informatics and StatisticsMelbourneAustralia

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