A generalized bivariate copula for flood analysis in Peninsular Malaysia


  • Izzat Fakhruddin Kamaruzaman Multimedia University http://orcid.org/0000-0003-0480-421X
  • Wan Zawiah Wan Zin Universiti Kebangsaan Malaysia
  • Noratiqah Mohd Ariff Universiti Kebangsaan Malaysia




Archimedean Copula, Elliptical Copula, Multivariate Distribution, Hydrology


This study generalized the best copula to characterize the joint probability distribution between rainfall severity and duration in Peninsular Malaysia using two dimensional copulas. Specifically, to construct copulas, Inference Function for Margins (IFM) and Canonical Maximum Likelihood (CML) methods were specially exploited. For the purpose of achieving copula fitting, the derived rainfall variables by making use of the Standardized Precipitation Index (SPI) were fitted into several distributions. Five copulas, namely Gaussian, Clayton, Frank, Joe and Gumbel were put to the tests to establish the best data fitted copula. The tests produced acknowledged and satisfactory results of copula fitting for rainfall severity and duration. Surveying the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), only three copulas produced a better fit for parametric and semi parametric approaches. Finally, two consistency tests were conducted and the results shown that Frank Copula produced consistent results.

Author Biographies

Izzat Fakhruddin Kamaruzaman, Multimedia University

Faculty of Business

Wan Zawiah Wan Zin, Universiti Kebangsaan Malaysia

School of Mathematical Sciences, Faculty of Science and Technology

Noratiqah Mohd Ariff, Universiti Kebangsaan Malaysia

School of Mathematical Sciences, Faculty of Science and Technology


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