A review of bivariate gamma distributions for hydrological application

Journal of Hydrology

Volumn 246, Issue 1-4, 2001, Pages 1-18

  Yue, S ^a   Ouarda, T B M J ^b   Bobee B ^b  

^a ENVIRONMENT CANADA   (Canada)

^b CENTRE EAU TERRE ENVIRONNEMENT   (Canada)

Author keywords

Bivariate gamma distribution; Correlation; Gamma distribution; Joint distribution; Marginal distribution; Multivariate frequency analysis

Indexed keywords

FLOODS; MODELS; PROBABILITY DISTRIBUTIONS;

GAMMA DISTRIBUTIONS;

HYDROLOGY;

HYDROLOGY; PROBABILITY;

EID: 0035371278     PISSN: 00221694     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-1694(01)00374-2     Document Type: Review

References (48)

1. Adamson P.T., Metcalfe A.V., Parmentier B. Bivariate extreme value distributions: an application of the Gibbs sampler to the analysis of floods. Water Resour. Res. 35:(9):1999;2825-2832.
2. Ashkar, F., 1980. Partial duration series models for flood analysis. PhD thesis, Ecole Polytechnique of Montreal, Montreal, Canada.
3. Ashkar F., El-Jabi N., Issa M. A bivariate analysis of the volume and duration of low-flow events. Stochastic Hydrology and Hydraulics. 12:1998;97-116.
4. Bacchi B., Becciu G., Kottegoda N.T. Bivariate exponential model applied to intensities and durations of extreme rainfall. J. of Hydrol. 155:1994;225-236.
5. Blokhinov, Y.G., Sarmanov, I.O., 1968. Gamma correlation and its use in computations of long-term streamflow regulation. Soviet Hydrology: Selected Papers, No. 1, 36-54.
6. Bobée B., Ashkar F. The Gamma Family and Derived Distributions Applied in Hydrology. 1991;Water Resources Publications, USA.
7. Cherian K.C. A bi-variate correlated gamma-type distribution function. Journal of Indian Math. Soc. 5:1941;133-144.
8. Choulakian V., El-Jabi N., Moussi J. On the distribution of flood volume in partial duration series analysis of flood phenomena. Stochastic Hydrology and Hydraulics. 4:1990;217-226.
9. Chow, V.T., 1953. Frequency analysis of hydrological data with special application to rainfall intensities. Univ. Illinois, Eng. Exper. Stat. Bull. 414.
10. Clarke R.T. Bivariate gamma distributions for extending annual streamflow records from precipitation: some large-sample results. Water Resour. Res. 16:(5):1980;863-870.
11. Correia F.N. Multivariate partial duration series in flood risk analysis. Singh V.P. Hydrologic Frequency Modelling. 1987;541-554 Reidel, Dordrecht, The Netherlands.
12. Crovelli, R.A., 1973. A bivariate precipitation model, paper presented at 3rd Conference on Proba. and Stat. in Atmospheric Science, 130-134, American Meteorological Society, Boulder, Colorado, USA.
13. Devroya L. Non-Uniform Random Variate Generation. 1986;Springer-Verlag, New York, USA.
14. Durrans S.R. Total probability methods for problems in flood frequency estimation. Parent E., Hubert P., Bobee B., Miquel J. Statistical and Bayesian Methods in Hydrological Science. International Hydrological Programme, Technical Documents in Hydrology, No. 20. 1998;299-326 UNESCO, Paris. chapter 18.
15. Farlie D.J.G. The performance of some correlated coefficients for a general bivariate distribution. Biometrika. 47:(3):1960;307-323.
16. Goel N.K., Seth S.M., Chandra S. Multivariate modeling of flood flows. ASCE, J. of Hydraulic Engineering. 124:(2):1998;146-155.
17. Goel N.K., Kurothe R.S., Mathur B.S., Vogel R.M. A derived flood frequency distribution for correlated rainfall intensity and duration. J. of Hydrology. 228:2000;56-67.
18. Gumbel E.J. Distributions a plusieurs variables don't les marges sont donnees. Comptes Rendus de l'Academie des Science, Paris. 246:1958;2717-2720.
19. Gupta A.K. On the expansion of bivariate gamma distribution. J. of the Indian Statistical Association. 17:1979;41-50.
20. Hashino M. Formulation of the joint return period of two hydrologic variates associated with a Poisson process. J. of Hydroscience and Hydraulic Engineering. 3:(2):1985;73-84.
21. Izawa T. The bivariate gamma distribution. Climate and Statistics. 4:(1):1953;9-15. (in Japanese).
22. Johnson N.L., Kotz S. Distributions in Statistics: Continuous Multivariate Distributions. 1972;John Wiley & Sons, New York.
23. Kanji G.K. 100 Statistical Tests. 1993;SAGE Publications.
24. Kelly K.S., Krzysztofowicz R. A bivariate meta-Gaussian density for use in hydrology. Stochastic Hydrology and Hydraulics. 11:1997;17-31.
25. Kibble W.F. A two-variate gamma type distribution. Sankhya. 5:1941;137-150.
26. Krstanovic P.F., Singh V.P. A multivariate stochastic flood analysis using entropy. Singh V.P. Hydrologic Frequency Modelling. 1987;515-539 Reidel, Dordrecht, The Netherlands.
27. Kurothe R.S., Goel N.K., Mathur B.S. Derived flood frequency distribution for negatively correlated rainfall intensity and duration. Water Resources Research. 33:1997;2103-2107.
28. Lall U., Bosworth K. Multivariate kernel estimation of functions of space and time. Hipel K.V., Mcleod A.I., Panu U.S., Singh V.P. Time Series Analysis in Hydrology and Environmental Engineering. 1994;301-315 Kluwer Academic Publications, Dordrecht, The Netherlands.
29. Loganathan G.V., Kuo C.Y., Yannaccone J. Joint probability distribution of streamflows and tides in estuaries. Nordic Hydrology. 18:1987;237-246.
30. Long D., Krzysztofowicz R. Farlie-Gumbel-Morgenstern bivariate densities: are they applicable in hydrology? Stochastic Hydrol. & Hydraul. 6:1992;47-54.
31. McKay A.T. Sampling from batches. J. Royal Stat. Society, B. 1:1934;207-216.
32. Moran P.A.P. Statistical inference with bivariate gamma distributions. Biometrika. 56:1969;627-634.
33. Morgenstern D. Einfache beispiele zweidimensionaler verteilungen. Mitteilungeblatt fur mathematische statistik. Wuezburg. 8:(3):1956;234-235.
34. Nagao, M., 1975. Multivariate probability distributions in statistical hydrology: Bivariate statistics as a center. In: Summer Training Conference on Hydraulics, Hydraulic Committee of Japanese Society of Civil Engineering, Hydraulics Series 75-A-4: 1-19 (in Japanese).
35. Nagao M., Kadoya M. The study on bivariate gamma distribution and its applicability (1). Annuals of the Disaster Prevention Research Institute of Kyoto University. 13B:1970;105-115. (in Japanese with English synopsis).
36. Nagao M., Kadoya M. Two-variate exponential distribution and its numerical table for engineering application. Bulletin of the Disaster Prevention Research Institute, Kyoto University. 20:(3):1971;183-215.
37. Sackl B., Bergmann H. A bivariate flood model and its application. Singh V.P. Hydrologic Frequency Modelling. 1987;571-582 Dordrecht, The Netherlands, Reidel.
38. Sarmanov, I.O., 1971. New forms of correlation relationships between positive quantities applied in hydrology. Paper presented at International Symposium on Mathematical Models in Hydrology, International Association of Scientific Hydrology, Warsaw, Poland, pp. 104-109.
39. Schucany W.R., Parr W.C., Boyer J.E. Correlation structure in Farlie-Gumbel-Morgenstern distributions. Biometrika. 65:(3):1978;650-653.
40. Singh K., Singh V.P. Derivation of bivariate probability density functions with exponential marginals. J. of Stochastic Hydrology and Hydraulics. 5:1991;55-68.
41. Smith, O.E., Adelfang, S.I., Tubbs, J.D., 1982. A bivariate gamma probability distribution with application to gust model, NASA Technical Memorandum 82483, National Aeronautics and Space Administration.
42. Stedinger J.R., Vogel R.M., Foufoula-Georgiou E. Frequency analysis of extreme events. Maidment D.R. Handbook of Hydrology. 1993;McGraw-Hill, Inc. chapter 18.
43. Weibull, W., 1939. A statistical theory of the Strength of materials. IngeniorsVetenskaps Akademiens-Handlingar, vol. 151. Stockholm. (The Royal Swedish Institute for Engineering Research Proceedings).
44. Wilks D.S. Multisite generalization of a daily stochastic precipitation generation model. J. of Hydrol. 210:1998;178-191.
45. Yue S. Applying bivariate normal distribution to flood frequency analysis. Water International. 24:(3):1999;248-254.
46. Yue S. Joint probability distribution of annual maximum storm peaks and amounts as represented by daily rainfalls. Hydrological Science Journal. 45:(2):2000;315-326.
47. Yue, S., 2000b. Applicability of the Nagao-Kadoya bivariate exponential distribution for modeling two correlated exponentially distributed variates. Stochastic Environmental Research and Risk Analysis (SERRA) (in press).
48. Yue S., Ouarda T.B.M.J., Bobée B., Legendre P., Bruneau P. The Gumbel mixed model for flood frequency analysis. J. of Hydrology. 226:1999;88-100.