Water Resour Manage (2014) 28:4835–4856 DOI 10.1007/s11269-014-0779-8 Analysis of Rainfall Severity and Duration in Victoria, Australia using Non-parametric Copulas and Marginal Distributions Ummul Fahri Abdul Rauf · Panlop Zeephongsekul Abstract The analysis of joint probability distributions of rainfall characteristics such as severity and duration is important in water resources management. Deriving their distri- butions using standard statistical techniques are often problematical due to its complexity. Standard methods usually assume that the rainfall characteristics are independent or that their marginal distributions belong to the same family of distributions. The use of copu- las based methodologies can circumvent these restrictions and are therefore increasingly popular. However, the copulas and marginal distributions that are commonly used belong to specific parametric families and their adoption could lead to spurious inferences if the underlying assumptions are violated. For this reason, we recommend a nonparamet- ric or semiparametric approach to estimate the joint distribution of rainfall characteristics. In this paper, we introduce and compare several copula–based approaches, each involv- ing a combination of parametric or nonparametric marginal distributions conjoined by a parametric or nonparametric copula. An empirical illustration of the different approaches using rainfall data collected from six stations in the state of Victoria, Australia, demon- strated that a nonparametric approach can often give better results than a purely parametric approach. Keywords Copulas · Parametric and nonparametric approaches · Rainfall severity and duration U. F. Abdul Rauf · P. Zeephongsekul () School of Mathematical and Geospatial Sciences, RMIT University, Victoria, 3000, Australia e-mail: panlop.zeephongsekul@rmit.edu.au Present Address: U. F. Abdul Rauf Centre for Foundation Studies, National Defence University of Malaysia, Sungai Besi Camp, 57000 Kuala Lumpur, Malaysia e-mail: ummul@upnm.edu.my; ummulfahri.abdulrauf@rmit.edu.au Received: 22 April 2014 / Accepted: 18 August 2014 / Published online: 5 September 2014 © Springer Science+Business Media Dordrecht 2014