A bivariate meta-Gaussian density for use in hydrology

• Abramowitz, M.; Stegun, I.A. (eds) 1972: Handbook of Mathematical Functions. New York: Dover Publications

  Google Scholar 

• Aitchison, J. 1986: The Statistical Analysis of Compositional Data. New York: Chapman and Hall

  Google Scholar 

• Barlow, R.E.: Proschan, F. 1975: Statistical Theory of Reliability and Life Testing: Probability Models. New York: Holt, Rinehart and Winston

  Google Scholar 

• Choulakian, V.; El-Jabi, N.; Moussi, J. 1990: On the distribution of flood volume in partial duration series analysis of flood phenomena. Stochastic Hydrology and Hydraulics 4, 217–226

  Article  Google Scholar 

• Dall'Aglio, G.; Kotz, S.; Salinetti, G. (Eds) 1991: Advances in Probability Distributions with Given Marginals. Dordrecht, The Netherlands: Kluwer Academic Publishers

  Google Scholar 

• Ekanayake, S.T.; Cruise, J.F. 1993: Comparisons of Weibull- and exponential-based partial duration stochastic flood models. Stochastic Hydrology and Hydraulics 7, 283–297

  Article  Google Scholar 

• Farlie, D.J.G. 1960: The performance of some correlation coefficients for a general bivariate distribution. Biometrika 47(3), 307–323

  Article  Google Scholar 

• Genest, C. 1987: Frank's family of bivariate distributions. Biometrika 74(3), 549–555

  Article  Google Scholar 

• Genest, C.; MacKay, J. 1986: The joy of copulas: bivariate distributions with uniform marginals. The American Statistician 40, 280–283

  Article  Google Scholar 

• Gibbons, J.D.; Chakraborti, S. 1992: Nonparametric Statistical Inference. New York: Marcel Dekker

  Google Scholar 

• Hosking, J.R.M.; Wallis, J.R. 1988: The effect of intersite dependence on regional flood frequency analysis. Water Resources Research 24(4), 588–600

  Google Scholar 

• Jouini, M.N.; Clemen, R.T. 1996: Copula models for aggregating expert opinions. Operations Research 44(3), 444–457

  Article  Google Scholar 

• Kibble, W. F. 1941: A two-variate gamma-type distribution. Sankhya 5, 137–150

  Google Scholar 

• Kruskal, W.H. 1958: Ordinal measures of association. Journal of the American Statistical Association 53(284), 814–861

  Article  Google Scholar 

• Krzysztofowicz, R.; Reese, S. 1993: Stochastic bifurcation processes and distributions of fractions. J. Amer. Stat. Assoc. 88(421), 345–354

  Article  Google Scholar 

• Krzysztofowicz, R.; Kelly, K.S. 1995: A meta-Gaussian distribution with specified marginals. Working paper, University of Virginia, Thornton Hall, Charlottesville, Virginia, 22903

  Google Scholar 

• Lehmann, E.L. 1966: Some concepts of dependence. Annals of Mathematical Statistics 37, 1137–1153

  Google Scholar 

• Long, D.; Krzysztofowicz, R. 1992: Farlie-Gumbel-Morgenstern bivariate densities: Are they applicable in hydrology? Stochastic Hydrology and Hydraulics 6, 47–54

  Article  Google Scholar 

• Long, D.; Krzysztofowicz, R. 1995: A family of bivariate densities constructed from marginals. Journal of the American Statistical Association 90(430), 739–746

  Article  Google Scholar 

• Marshall, A.W.; Olkin, I. 1967: A multivariate exponential distribution. Journal of the American Statistical Association 62(317), 30–44

  Article  Google Scholar 

• Moran, P.A.P. 1969: Statistical inference with bivariate distributions. Biometrika 56(3), 627–634

  Article  Google Scholar 

• Moran, P.A.P. 1970: Simulation and evaluation of complex water systems operations. Water Resour. Res. 6(6), 1737–1742

  Google Scholar 

• Owen, D.B. 1956: Tables for computing bivariate normal probabilities. Annals of Mathematical Statistics 27, 1075–1090

  Google Scholar 

• Rosbjerg, D. 1987: On the annual maximum distribution in dependent partial duration series. Stochastic Hydrology and Hydraulics 1, 3–16

  Article  Google Scholar 

• Schucany, W.R.; Parr, W.C.; Boyer, J.E. 1978: Correlation structure in Farlie-Gumbel-Morgenstern distributions. Biometrika 65(3), 650–653

  Article  Google Scholar 

• Singh, K.; Singh, V.P. 1991: Derivation of bivariate probability density functions with exponential marginals. Stochastic Hydrology and Hydraulics 5, 55–68

  Article  Google Scholar 

• Warren, D. 1992: A multivariate gamma distribution arising from a Markov model. Stochastic Hydrology and Hydraulics 6, 183–190

  Article  Google Scholar 

Download references