Using the skew-t copula to model bivariate rainfall distribution

We simulate monthly rainfall at two sites in the Murray--Darling Basin. In order to construct a suitable joint distribution, we model the individual totals using appropriate gamma distributions and use a multivariate skew-t distribution to construct an appropriate copula. The skew-t distribution is considered robust as it includes both skewness and tail dependence structure and allows us to model correlations. We investigate the characteristics of a bivariate skew-t distribution and show how adjusting the parameters generates simulated data which matches the observed data. References A. Azzalini. R package sn: The skew-normal and skew-$t$ distributions (version 0.4-12). Universita di Padova, Italia, 2009. http://azzalini.stat.unipd.it/SN. A. Azzalini and A. Capitanio. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution. Journal of the Royal Statistical Society: Series B, 65(2):367--389, 2003. http://www.blackwell-synergy.com/doi/abs/10.1111/1467-9868.00391. A. Azzalini and M. G. Genton. Robust likelihood methods based on the skew-t and related distributions. International Statistical Review, 76(1):106--129, 2008. http://dx.doi.org/10.1111/j.1751-5823.2007.00016.x. P. Embrechts, F. Lindskog, and A. Mc Neil. Modelling Dependence with Copulas and Applications to Risk Management In: Handbook of Heavy Tailed Distributions in Finance, chapter 8, pages 329--384. Elsevier, 2003. C. Genest and A.-C. Favre. Everything you always wanted to know about copula modelling but were afraid to ask. Journal of Hydrologic Engineering, 12(4):347--368, 2007. http://dx.doi.org/10.1061/(ASCE)1084-0699(2007)12:4(347). R. B. Nelsen. An Introduction to Copulas. Springer, New York, 2nd edition, 2006. Murray-Darling Basin Authority. http://www.mdba.gov.au, 2008. [accessed 10-Jan-2010]. G. Wong, M. F. Lambert, M. Leonard, and A. Metcalfe. Drought analysis using trivariate copulas conditional on climatic states. Journal of Hydrologic Engineering, 15(2):129--141, 2010. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000169