Volume 6 Issue 1
Jan.  2013
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Article Navigation >  Water Science and Engineering  > 2013  >  6(1): 18-30
Ming-wei MA, Li-liang REN, Song-bai SONG, Jia-li SONG, Shan-hu JIANG. 2013: Goodness-of-fit tests for multi-dimensional copulas: Expanding application to historical drought data. Water Science and Engineering, 6(1): 18-30. doi: 10.3882/j.issn.1674-2370.2013.01.002
Citation: Ming-wei MA, Li-liang REN, Song-bai SONG, Jia-li SONG, Shan-hu JIANG. 2013: Goodness-of-fit tests for multi-dimensional copulas: Expanding application to historical drought data. Water Science and Engineering, 6(1): 18-30. doi: 10.3882/j.issn.1674-2370.2013.01.002
shu

Goodness-of-fit tests for multi-dimensional copulas: Expanding application to historical drought data

doi: 10.3882/j.issn.1674-2370.2013.01.002
  • 1.

    State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, P. R. China

  • 2.

    College of Water Resources and Architectural Engineering, Northwest A&F University, Yangling 712100, P. R. China

  • 3.

    Business School, Hohai University, Nanjing 211100, P. R. China

Funds:  This work was supported by the Program of Introducing Talents of Disciplines to Universities of the Ministry of Education and State Administration of the Foreign Experts Affairs of China (the 111 Project, Grant No. B08048) and the Special Basic Research Fund for Methodology in Hydrology of the Ministry of Sciences and Technology of China (Grant No. 2011IM011000).
More Information
  • Corresponding author: Li-liang REN
  • Received Date: 2011-12-02
  • Rev Recd Date: 2012-04-21
    Abstract
  • The question of how to choose a copula model that best fits a given dataset is a predominant limitation of the copula approach, and the present study aims to investigate the techniques of goodness-of-fit tests for multi-dimensional copulas. A goodness-of-fit test based on Rosenblatt’s transformation was mathematically expanded from two dimensions to three dimensions and procedures of a bootstrap version of the test were provided. Through stochastic copula simulation, an empirical application of historical drought data at the Lintong Gauge Station shows that the goodness-of-fit tests perform well, revealing that both trivariate Gaussian and Student t copulas are acceptable for modeling the dependence structures of the observed drought duration, severity, and peak. The goodness-of-fit tests for multi-dimensional copulas can provide further support and help a lot in the potential applications of a wider range of copulas to describe the associations of correlated hydrological variables. However, for the application of copulas with the number of dimensions larger than three, more complicated computational efforts as well as exploration and parameterization of corresponding copulas are required.

     

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