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Analysis of Rainfall Severity and Duration in Victoria, Australia using Non-parametric Copulas and Marginal Distributions

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Abstract

The analysis of joint probability distributions of rainfall characteristics such as severity and duration is important in water resources management. Deriving their distributions 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 copulas 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 nonparametric or semiparametric approach to estimate the joint distribution of rainfall characteristics. In this paper, we introduce and compare several copula–based approaches, each involving 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, demonstrated that a nonparametric approach can often give better results than a purely parametric approach.

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Acknowledgments

The authors sincerely acknowledge the Bureau of Meteorology (BOM), Australia, for providing the complete monthly precipitation data that been used in this study. The work is financed by SLAB Scholarship provided by the Ministry of Higher Education of Malaysia and National Defence University of Malaysia.

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Correspondence to Panlop Zeephongsekul.

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Abdul Rauf, U.F., Zeephongsekul, P. Analysis of Rainfall Severity and Duration in Victoria, Australia using Non-parametric Copulas and Marginal Distributions. Water Resour Manage 28, 4835–4856 (2014). https://doi.org/10.1007/s11269-014-0779-8

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  • DOI: https://doi.org/10.1007/s11269-014-0779-8

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