×

A software review for extreme value analysis. (English) Zbl 1329.62027

Summary: 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.

MSC:

62-04 Software, source code, etc. for problems pertaining to statistics
60G70 Extreme value theory; extremal stochastic processes
62G32 Statistics of extreme values; tail inference

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) · Zbl 1207.62109 · doi:10.1016/j.jspi.2010.11.038
[2] Asquith, W.H.: lmomco: L-moments, Trimmed L-moments, L-comoments, and Many Distributions. R package version 0.97.4 ed. (2009)
[3] Beirlant, J., Goegebeur, Y., Segers, J., Teugels, J.: Statistics of Extremes. Wiley, Chichester (2004)
[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)
[5] Capéraà, P., Fougères, A.-L., Genest, C.: A non-parametric estimation procedure for bivariate extreme value copulas. Biometrika 84, 567–577 (1997) · Zbl 1058.62516 · doi:10.1093/biomet/84.3.567
[6] Coles, S.G.: An Introduction to Statistical Modeling of Extreme Values. Springer, London (2001) · Zbl 0980.62043
[7] Coles, S., Pauli, F.: Models and inference for uncertainty in extremal dependence. Biometrika 89, 183–196 (2002) · Zbl 0997.62041 · doi:10.1093/biomet/89.1.183
[8] Coles, S.G., Tawn, J.A.: Modelling extreme multivariate events. J. R. Stat. Soc. B 53, 377–392 (1991) · Zbl 0800.60020
[9] Coles, S.G., Heffernan, J.E., Tawn, J.A.: Dependence measures for extreme value analyses. Extremes 2, 339–365 (1999) · Zbl 0972.62030 · doi:10.1023/A:1009963131610
[10] Cooley, D., Nychka, D.W., Naveau, P.: Bayesian spatial modeling of extreme precipitation return levels. J. Am. Stat. Assoc. 102, 824–840 (2007) · Zbl 1469.62389 · doi:10.1198/016214506000000780
[11] Dalrymple, T.: Flood frequency analyses. Water Supply Paper 1543-A, U.S. Geological Survey, Reston, VA (1960)
[12] Davison, A.C., Padoan, S.A., Ribatet, M.: Statistical modelling of spatial extremes. Stat. Sci. 27(2), 161–186 (2012) · Zbl 1330.86021 · doi:10.1214/11-STS376
[13] de Haan, L.: A spectral representation for max-stable processes. Ann. Probab. 12, 1194–1204 (1984) · Zbl 0597.60050 · doi:10.1214/aop/1176993148
[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) · Zbl 1101.62002
[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) · Zbl 0701.62029 · doi:10.1214/aos/1176347397
[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)
[17] Diebolt, J., Garrido, M., Trottier, C.: Improving extremal fit: a Bayesian regularization procedure. Reliab. Eng. Syst. Saf. 82(1), 21–31 (2003b) · doi:10.1016/S0951-8320(03)00096-6
[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)
[19] Dietrich, D., de Haan, L., Hüsler, J.: Testing extreme value conditions. Extremes 5, 71–85 (2002) · Zbl 1035.60050 · doi:10.1023/A:1020934126695
[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) · Zbl 1093.62052
[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) · doi:10.1016/j.jhydrol.2008.02.011
[22] Embrechts, P., Klüppelberg, C., Mikosch, T.: Modelling Extremal Events for Insurance and Finance, 648pp. Springer, Berlin (1997) · Zbl 0873.62116
[23] Ferro, C.A.T., Segers, J.: Inference for clusters of extreme values. J. R. Stat. Soc. B 65, 545–556 (2003) · Zbl 1065.62091 · doi:10.1111/1467-9868.00401
[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) · Zbl 1079.91541 · doi:10.1162/10811820160080103
[25] Gilleland, E., Katz, R.W.: New software to analyze how extremes change over time. Eos 92(2), 13–14 (2011) · doi:10.1029/2011EO020001
[26] Heffernan, J.E.: A directory of coefficients of tail dependence. Extremes 3, 279–290 (2000) · Zbl 0979.62040 · doi:10.1023/A:1011459127975
[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) · Zbl 1046.62051 · doi:10.1111/j.1467-9868.2004.02050.x
[28] Hill, B.M.: A simple general approach to inference about the tail of a distribution. Ann. Stat. 3, 1163–1174 (1975) · Zbl 0323.62033 · doi:10.1214/aos/1176343247
[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) · Zbl 0703.62018
[30] Hosking, J.R.M.: L-moments, R package version 1.5 ed. (2009a)
[31] Hosking, J.R.M.: Regional frequency analysis using L-moments, R package version 2.2 ed. (2009b)
[32] Hosking, J.R.M., Wallis, J.R.: Parameter and quantile estimation for the Generalized Pareto distribution. Technometrics 29(3), 339–349 (1987) · Zbl 0628.62019 · doi:10.1080/00401706.1987.10488243
[33] Hosking, J.R.M., Wallis, J.R.: Regional Frequency Analysis: An Approach Based on L-Moments. Cambridge University Press, Cambridge (1997)
[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) · doi:10.1080/00401706.1985.10488049
[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) · Zbl 1164.62352 · doi:10.1007/s10687-006-0025-8
[37] Kabluchko, Z., Schlather, M., de Haan, L.: Stationary max-stable fields associated to negative definite functions. Ann. Probab. 37(5), 2042–2065 (2009) · Zbl 1208.60051 · doi:10.1214/09-AOP455
[38] Kojadinovic, I., Yan, J.: Modeling multivariate distributions with continuous margins using the copula R package. Journal of Statistical Software 34, 1–20 (2010) · doi:10.18637/jss.v034.i09
[39] Ledford, A.W., Tawn, J.A.: Statistics for near independence in multivariate extreme values. Biometrika 83, 169–187 (1996) · Zbl 0865.62040 · doi:10.1093/biomet/83.1.169
[40] Ledford, W.A., Tawn, J.A.: Modelling dependence within joint tail regions. J. R. Stat. Soc. B 59, 475–499 (1997) · Zbl 0886.62063 · doi:10.1111/1467-9868.00080
[41] McCulloch, J.H.: Simple consistent estimators of stable distribution parameters. Commun. Stat., Simul. Comput. 15, 1109–1136 (1986) · Zbl 0612.62028 · doi:10.1080/03610918608812563
[42] McNeil, A., Stephenson, A.G.: evir: extreme values in R (2008)
[43] Nolan, J.P.: Stable Distributions–Models for Heavy Tailed Data, 352pp. Birkhauser, Boston (2007). ISBN-13: 9780817641597
[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 · Zbl 1329.60157 · doi:10.1007/s10687-011-0128-8
[45] Pickands, J.: Statistical inference using extreme order statistics. Ann. Stat. 3, 119–131 (1975) · Zbl 0312.62038 · doi:10.1214/aos/1176343003
[46] Pickands, J.: Multivariate extreme value distributions. In: Proc. 43rd Sess. Int. Statist. Inst., vol. 49, pp. 859–878 (1981) · Zbl 0518.62045
[47] R Development Core Team: R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria (2012). ISBN 3-900051-07-0
[48] Reiss, R.D., Thomas, M.: Statistical Analysis of Extreme Values, From Insurance, Finance Hydrology and Other Fields. Birkhauser, New York (2001) · Zbl 1002.62002
[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) · Zbl 1122.62036
[50] Ribatet, M.: POT: Generalized Pareto Distribution and Peaks Over Threshold, R package verions 1.1-0 ed. (2009)
[51] Ribatet, M.: SpatialExtremes: Modelling Spatial Extremes, R package version 1.8-5 (2011)
[52] Rootzén, H., Tajvidi, N.: Multivariate generalized Pareto distributions. Bernoulli 12(5), 917–930 (2006) · Zbl 1134.62028 · doi:10.3150/bj/1161614952
[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) · Zbl 1248.62156 · doi:10.1111/j.1467-9868.2008.00700.x
[54] Schlather, M.: Models for stationary max-stable random fields. Extremes 5(1), 33–44 (2002) · Zbl 1035.60054 · doi:10.1023/A:1020977924878
[55] Smith, R.L.: Maximum likelihood estimation in a class of non-regular cases. Biometrika 72, 67–90 (1985) · Zbl 0583.62026 · doi:10.1093/biomet/72.1.67
[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)
[58] Southworth, H., Heffernan, J.E.: texmex: Threshold exceedences and multivariate extremes, R package version 1.0 (2010)
[59] Stephenson, A.G.: evd: extreme value distributions. R News 2(2), 31–32 (2002)
[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)
[61] Stephenson, A.G., Gilleland, E.: Software for the analysis of extreme events: the current state and future directions. Extremes 8, 87–109 (2005) · Zbl 1114.62002 · doi:10.1007/s10687-006-7962-0
[62] Stephenson, A.G., Ribatet, M.: evdbayes: Bayesian analysis in extreme value theory, R package version 1.0-8 ed. (2010)
[63] Stephenson, A.G., Tawn, J.A.: Bayesian inference for extremes: accounting for the three extremal types. Extremes 7, 291–307 (2004) · Zbl 1090.62025 · doi:10.1007/s10687-004-3479-6
[64] van der Loo, M.P.J.: Distribution Based Outlier Detection for Univariate Data. Statistics Netherlands, The Hague (2010)
[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)
[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) · Zbl 1268.62048
[67] Wuertz, D.: fExtremes: Rmetrics–Extreme Financial Market Data, R package version 2100.77 ed. (2009)
[68] Yee, T.W.: The VGAM package for categorical data analysis. Journal of Statistical Software 32, 1–34 (2010) · doi:10.18637/jss.v032.i10
[69] Yee, T.W., Stephenson, A.G.: Vector generalized linear and additive extreme value models. Extremes 10, 1–19 (2007) · Zbl 1150.62371 · doi:10.1007/s10687-007-0032-4
[70] Yee, T.W., Wild, C.J.: Vector generalized additive models. J. R. Stat. Soc. B 58, 481–493 (1996) · Zbl 0855.62059
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.