1,330
Views
23
CrossRef citations to date
0
Altmetric
Original Articles

Trivariate generalized extreme value distribution in flood frequency analysis

Distribution trivariée généralisée des valeurs extrêmes pour l'analyse fréquentielle de crue

&
Pages 550-567 | Received 27 Jul 2006, Accepted 22 Feb 2008, Published online: 18 Jan 2010

REFERENCES

  • Anderson , T. W. 1957 . Maximum likelihood estimates for a multivariate Normal distribution when some observations are missing. . Am. Stat. Assoc. J. , 52 : 220 – 223 .
  • Andrews , D. F. 1972 . Plot of high dimensional data. . Biometrics , 28 : 125 – 136 .
  • Boes , D. C. 1983 . “ Class notes for ST530 Mathematical Statistics. ” . Fort Collins, Colorado, , USA : Department of Statistics, Colorado State University .
  • Clarke , R. T. 1980 . Bivariate gamma distributions for extending annual streamflow records from precipitation: some large sample results. . Water Resour. Res. , 16 ( 5 ) : 863 – 870 .
  • Cunnane , C. 1988 . Methods and merits of regional flood frequency analysis. . J. Hydrol. , 100 : 269 – 290 .
  • De Michele , C. , Salvadori , G. , Canossi , M. , Petaccia , A. and Rosso , R. 2005 . Bivariate statistical approach to check adequacy of dam spilway. . J. Hydrol. Engng ASCE , 10 ( 1 ) : 50 – 57 .
  • Escalante , C. 1998a . Multivariate estimation of extreme flood hydrographs. . Hydrol. Sci. Technol. AIH , 14 : 19 – 27 .
  • Escalante , C. 1998b . Multivariate extreme value distribution with mixed Gumbel marginals. . J. Am. Water Resour. Assoc. , 3 ( 2 ) : 321 – 333 .
  • Escalante , C. and Domínguez , J. 1997 . Parameter estimation for bivariate extreme value distribution by maximum entropy. . Hydrol. Sci. Technol. AIH , 13 : 1 – 10 .
  • Escalante , C. and Raynal , J. 1998 . Multivariate estimation of floods. The trivariate Gumbel distribution. . J. Statist. Comput. Simulation , 61 ( 4 ) : 313 – 340 .
  • Gumbel , E. J. 1959 . Multivariate distributions with given margins. . Revista da faculdade de Ciencias , 2 (2) : 178 – 218 . Serie A
  • Gumbel , E. J. 1960a . Multivariate extremal distributions. . Bull. Int. Statist. Inst. , 39 ( 2 ) : 471 – 475 .
  • Gumbel , E. J. 1960b . Distributions des valeurs extremes en plusiers dimensions. . Publ. Inst. Stat. Univ. Paris. , 9 : 171 – 173 .
  • Gumbel , E. J. and Mustafi , C. K. 1967 . Some analytical properties of bivariate extremal distributions. . Am. Statist. Assoc. J. , 62 : 569 – 589 .
  • Hann , C. T. 1977 . Statistical Methods in Hydrology. USA : The Iowa State University Press .
  • Hosking , J. R. M. and Wallis , J. R. 1997 . Regional Frequency Analysis. Cambridge, , UK : Cambridge University Press .
  • Jenkinson , A. F. 1955 . The frequency distribution of the annual maximum (or minimum) values of meteorological elements. . Quart. J. Roy. Met. Soc. , 87 : 158 – 171 .
  • Kendall , M. and Stuart , A. 1979 . The Advanced Theory of Statistics Vol. 2 , London, , UK : Macmillan .
  • Kite , G. W. 1988 . Frequency and Risk Analyses in Hydrology. Littleton, Colorado, , USA : Water Resources Publications .
  • Kuester , J. L. and Mize , J. H. 1973 . Optimization Techniques with FORTRAN. New York, , USA : McGraw-Hill .
  • Matalas , N. C. and Jacobs , B. 1964 . “ A correlation procedure for augmenting hydrologic data. ” . US Geol. Survey Prof. Paper 434-E, E1-E7.
  • Nathan , R. J. and McMahon , T. A. 1990 . Identification of homogeneous regions for the purposes or regionalisation. . J. Hydrol. , 121 : 217 – 238 .
  • O'Hara , H. and Smith , F. 1980 . The evaluation of the definite integrals by interval subdivision. . Computer J. , 12
  • Raynal , J. 1985 . “ Bivariate extreme value distributions applied to flood frequency analysis PhD. ” . Fort Collins, Colorado, , USA : Dissertation, Civil Engineering Department, Colorado State University .
  • Raynal-Villaseñor , J. A. and Salas , J. D. 1987 . “ Multivariate extreme value distributions in hydrological analyses. ” . In Water for the Future: Hydrology in Perspective , Edited by: Rodda , J. C. and Matalas , N. C. 111 – 119 . Wallingford, , UK : IAHS Publ. 164. IAHS Press . (Proc. Rome Symp., April 1987) (http://.iahs.info).
  • Rueda , E. 1981 . “ Transfer of information for flood related variables. ” . Fort Collins, Colorado, , USA : Civil Engineering Department, Colorado State Univ. . MSc Thesis
  • Singh , V. P. 1987 . Regional Flood Frequency Analysis. Edited by: Reidel , D. Dordrecht, , The Netherlands
  • Stroud , A. H. 1968 . Gaussian Quadrature Formulas. Englewood Cliffs, New Jersey, , USA : Prentice Hall .
  • Stroud , A. H. 1971 . Approximate Calculation of Multiple Integrals. New Jersey, , USA : Prentice Hall, Englewood Cliffs .
  • Yue , S. 1999 . Applying the bivariate normal distribution to flood frequency analysis. . Water Int. , 24 ( 3 ) : 248 – 252 .
  • Yue , S. 2000 . The bivariate lognormal distribution to model a multivariate flood episode. . Hydrol. Processes , 14 : 2575 – 2588 .
  • Yue , S. 2001 . A bivariate gamma distribution for use in multivariate flood frequency analysis. . Hydrol. Processes , 15 : 1033 – 1045 .
  • Yue , S. and Rasmussen , P. 2002 . Bivariate frequency analysis: discussion of some useful concepts in hydrological application. . Hydrol. Processes , 16 : 2881 – 2898 .

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.