Construction of bivariate asymmetric copulas

Saikat Mukherjee, Youngsaeng Lee, Jong Min Kim, Jun Jang, Jeong Soo Park

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    3 Scopus citations


    Copulas are a tool for constructing multivariate distributions and formalizing the dependence structure between random variables. From copula literature review, there are a few asymmetric copulas available so far while data collected from the real world often exhibit asymmetric nature. This necessitates developing asymmetric copulas. In this study, we discuss a method to construct a new class of bivariate asymmetric copulas based on products of symmetric (sometimes asymmetric) copulas with powered arguments in order to determine if the proposed construction can offer an added value for modeling asymmetric bivariate data. With these newly constructed copulas, we investigate dependence properties and measure of association between random variables. In addition, the test of symmetry of data and the estimation of hyper-parameters by the maximum likelihood method are discussed. With two real example such as car rental data and economic indicators data, we perform the goodness-of-fit test of our proposed asymmetric copulas. For these data, some of the proposed models turned out to be successful whereas the existing copulas were mostly unsuccessful. The method of presented here can be useful in fields such as finance, climate and social science.

    Original languageEnglish (US)
    Pages (from-to)217-234
    Number of pages18
    JournalCommunications for Statistical Applications and Methods
    Issue number2
    StatePublished - Mar 1 2018

    Bibliographical note

    Funding Information:
    This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1A2B4014518). Lee’s work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1A6A3A11032852).


    • Cramér-von Mises statistics
    • Empirical copula
    • Fourier copula
    • Maximum pseudolikelihood estimation
    • Parametric bootstrap
    • Pseudo-observations

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