2,243
Views
14
CrossRef citations to date
0
Altmetric
Original Articles

Modélisation de la structure de dépendance hauteur—durée d'événements pluvieux par la copule de Gumbel

Modelling the dependence structure of rainfall depth and duration by Gumbel's copula

&
Pages 802-817 | Received 14 Jun 2006, Accepted 18 Feb 2008, Published online: 18 Jan 2010

REFERENCES

  • Abberger , K. 2005 . A simple graphical method to explore tail-dependence in stock-return pairs. . Applied Financial Economics , 15 : 43 – 51 .
  • Belguise , O. 2001 . “ Tempêtes: étude des dépendances entre les branches auto et incendie avec la théorie des copulas. Mémoire DUAS troisième année. Actuariat ” . Strasbourg, , France : Univ. Louis Pasteur .
  • Bendjoudi , H. , Hubert , P. , Schertzer , D. and Lovejoy , S. 1997 . Interprétation multifractale des courbes intensité-durée-fréquence des précipitations. . C. R. Acad. Sci. Paris , 325 : 323 – 326 .
  • Burlando , P. and Rosso , R. 1996 . Scaling and multiscaling models of depth-duration-frequency curves for storm precipitation. . J. Hydrol. , 187 : 45 – 64 .
  • Charpentier , A. 2003 . “ Tail distribution and dependence measures. ” . In Proceedings ASTIN (Actuarial Studies in Non-life Insurance. Berlin http://www.actuaries.org/ASTIN/Colloquia/Berlin/Charpentier.pdf.
  • D'Agostino , R. and Stephens , M. 1986 . Goodness-of-Fit Techniques 235 – 277 . New York, , USA : Marcel Dekker .
  • Day , J. A. 2005 . The Book of Clouds. New York, , USA : Sterling Publishing Company, Inc. .
  • De Michele , C. , Kottegoda , N. T. and Rosso , R. 2001 . The derivation of areal reduction factor of storm rainfall from its scaling properties. . Water Resour. Res. , 37 ( 12 ) : 3247 – 3252 .
  • De Michele , C. , Kottegoda , N. T. and Rosso , R. 2002 . IDAF curves of extreme storm rainfall: A scaling approach. . Water Sci. & Tech. , 45 ( 2 ) : 83 – 90 .
  • De Michele , C. and Salvadori , G. 2003 . A generalized pareto intensity-duration model of storm rainfall exploiting 2-copulas. . J. Geophys. Res. , 108 ( D2 ) 15-1-15-2.
  • De Michele , C. , Salvadori , G. , Canossi , M. , Petaccia , A. and Rosso , R. 2005 . Bivariate statistical approach to spillway design flood. . J. Hydrol. Engng ASCE , 10 ( 1 ) : 50 – 57 .
  • Denuit , M. and Charpentier , A. 2004 . Mathématiques de l'Assurance Non-Vie—Concepts fondamentaux de la théorie du risque. Paris, , France : tome 1. Economica . Collection «Économie et Statistiques Avancées»
  • Embrechts , P. , Lindskog , F. and McNeil , A. J. 2003 . “ Modelling dependence with copulas and applications to risk management. ” . In Handbook of Heavy Tailed Distributions in Finance 329 – 384 . New York, , USA : Elsevier Sciences .
  • Favre , A. C. , El Adlouni , S. , Perreault , T. L. , Thiemonge , N. and Bobée , B. 2004 . Multivariate hydrological frequency analysis using copulas. . Water Resour. Res. , 40 : 1 – 12 . W01101
  • Fisher , N. I. and Switzer , P. 1985 . Chi-plots for assessing dependence. . Biometrika. , 72 : 253 – 265 .
  • Fisher , N. I. and Switzer , P. 2001 . Graphical assessment of dependence: is a picture worth 100 tests? . Amer. Statist. , 55 : 233 – 239 .
  • Frees , E. W and Valdez , E. A. 1998 . Understanding relationships using copulas. . N. Am. Actuarial J. , 2 ( 1 ) : 1 – 25 .
  • Genest , C. and Boies , J. C. 2003 . Detecting dependence with Kendall plots. . Amer. Statist. , 57 : 275 – 284 .
  • Genest , C. and Favre , A. C. 2007 . Everything you always wanted to know about copula modeling but were afraid to ask. . J. Hydrol. Engng ASCE , 12 : 347 – 368 .
  • Genest , C. and Mackay , R. J. 1986 . Copules archimédiennes et familles de lois bidimensionnelles dont les marges sont données. . Rev. Can. Stat. , 14 : 145 – 159 .
  • Genest , C. , Quessy , J. F. and Rémillard , B. 2006 . Goodness-of-fit procedures for copula models based on the probability integral transformation. . Scand. J. Statist. , 33 ( 2 ) : 337 – 366 .
  • Genest , C. and Rivest , L. 1993 . Statistical inference procedures for bivariate Archimedean copulas. . J. Am. Statis. Assoc. , 88 : 1034 – 1043 .
  • Giles , D. E. A. 2000 . “ A saddlepoint approximation to the distribution function of the Anderson-Darling test statistic. ” . In Econ. Work. Paper EWP 0005 Victoria, , Canada : University of Victoria. . ISBN 1485-6441.
  • Goel , N. K. , Kurothe , R. S. , Mathur , B. S. and Vogel , R. M. 2000 . A derived flood frequency distribution for correlated rainfall intensity and duration. . J. Hydrol. , 228 : 56 – 67 .
  • Grimaldi , S. , Serinaldi , F. , Napolitano , F. and Ubertini , L. 2005 . “ A 3-copula function application for design hyetograph analysis. ” . In Sustainable Water Management Solutions for Large Cities Edited by: Savic , D. A. , Mariño , M. A. , Savenije , H. H. G. and Bertoni , J. C. 203 – 212 . Wallingford, , UK : IAHS Publ. 293. IAHS Press .
  • Hürlimann , W. 2004 . Fitting bivariate cumulative returns with copulas . Comp. Statis. Data Anal. , 45 : 355 – 372 .
  • Joe , H. 1997 . Multivariate Models and Dependence Concepts. London, , UK : Monographs on Statistics and Applied Probability, Chapman & Hall .
  • Johnson , N. L. , Kotz , S. and Balakrishnan , N. 1994 . Continuous Univariate Distributions 348 – 351 . Chichester, , UK : John Wiley & Sons . vol. 2 (second edn)
  • Klugman , A. S. and Parsa , R. 1999 . Fitting bivariate loss distribution with copulas. . Inst. Math. Econ. , 24 : 139 – 148 .
  • Kurothe , R. S. , Goel , N. K. and Mathur , B. S. 1997 . Derived flood frequency distribution for negatively correlated rainfall intensity and duration. . Water Resour. Res. , 33 ( 9 ) : 2103 – 2107 .
  • Nadarajah , S. and Kotz , S . 2006 . Discussion of “Models for extremes using the extended tree-parameter Burr XII system with application to flood frequency analysis”, On the extended Burr XII distribution. . Hydrol. Sci. J. , 51 ( 6 ) : 1203 – 1204 .
  • Nelsen , R. B. 1999 . An Introduction to Copulas. New York, , USA : Springer .
  • Roncalli , T. 2002 . “ Théorie des valeurs extrêmes. ” . France : DESS, Université Paris IX Dauphine .
  • Salvadori , G. and De Michele , C. 2004a . Analytical calculation of storm volume statistics involving Pareto-like intensity-duration marginals. . Geophys. Res Lett. , 31 L04502, doi:10.1029/2003GL018767.
  • Salvadori , G. and De Michele , C. 2004b . Frequency analysis via copulas: theoretical aspects and applications to hydrological events. . Water. Resour. Res. , 40 W12511, doi:10.1029/2004WR003133.
  • Salvadori , G. and De Michele , C. 2006 . Statistical characterization of temporal structure of storms. . Adv. Water. Resour. , 6 : 827 – 842 .
  • Schweizer , B. 1991 . “ Thirty years of copulas. ” . In Advances in Probability Distributions with Given Marginals: Beyond the Copulas, Mathematics and Its Applications Edited by: Dall'Aglio , G. , Kotz , S. and Salinetti , G. 13 – 50 . Dordrecth, , The Netherlands : Kluwer Academic Publishers .
  • Schweizer , B. and Sklar , A. 1983 . Probabilistic Metric Spaces. Amsterdam, , The Netherlands : Elsevier .
  • Silvapulle , P. and Zhang , X. 2006 . “ Assessing dependence changes in the Asian financial market returns using plots based on nonparametric measures. ” . Monash, , Australia : Series Monash Econ. Busin. Statist. Working Papers 9–06, Monash University, Department of Econometrics and Business Statistics .
  • Shao , Q. 2004 . Notes on maximum likelihood estimation for the three-parameter Burr XII distribution. . Comp. Statist. Data. Anal. , 45 : 675 – 687 .
  • Shao , Q. , Wong , H. , Xia , J. and Ip , W.-C. 2004 . Models for extremes using the extended tree-parameter Burr XII system with application to flood frequency analysis. . Hydrol. Sci. J. , 49 ( 4 ) : 685 – 702 .
  • Shao , Q. , Wong , H. , Xia , J. and Ip , W.-C. 2006 . Reply to “On the extended Burr XII distribution”. . Hydrol. Sci. J. , 51 ( 6 ) : 1204 – 1207 .
  • Sklar , A. 1959 . “ Fonctions de répartition à n dimensions et leurs marges. ” . In Publ. Inst. Statist. Vol. 8 , 229 – 231 . France : Université Paris VIII .
  • Veneziano , D. and Furcolo , P. 2002 . Multifractality of rainfall and scaling of intensity-duration-frequency curves. . Water Resour. Res. , 38 ( 12 ) : 1306 doi:10.1029/2001WR00372.
  • Veneziano , D. and Langousis , A. 2005 . The areal reduction factor: a multifractal analysis. . Water Resour. Res. , 41 W07008, doi:10.1029/2004WR003765.
  • Venter , G. 2002 . Tails of copulas. . Proc. Casualty Actuarial Society. , 89 : 68 – 113 .
  • Venter , G. 2003 . Quantifying correlated reinsurance exposures with copulas. . Casualty Actuarial Society Forum, Spring 2003 , : 215 – 229 .
  • Zhang , L. and Singh , V. P. 2006 . Bivariate flood frequency analysis using the copula method. . J. Hydrol. Engng , 11 ( 2 ) : 150 – 164 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.