Some results on truncation dependence invariant class of copulas

Engin A. Sungur

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    12 Scopus citations

    Abstract

    In this paper, m-dimensional distribution functions with truncation invariant dependence structure are studied. Some of the properties of generalized Archimedean class of copulas under this dependence structure are presented including some results on the conditions of compatibility. It has been shown that Archimedean copula generalized as it is described by Jouini and Clemen[1] which has the truncation invariant dependence structure has to have the form of independence or Cook-Johnson copula. We also consider a multi-parameter class of copulas derived from one-parameter Archimedean copulas. It has been shown that this class has a probabilistic meaning as a connecting copula of the truncated random pair with a right truncation region on the third variable. Multiparameter copulas generated in this paper stays in the Archimedean class. We provide formulas to compute Kendall's tau and explore the dependence behavior of this multi-parameter class through examples.

    Original languageEnglish (US)
    Pages (from-to)1399-1422
    Number of pages24
    JournalCommunications in Statistics - Theory and Methods
    Volume31
    Issue number8
    DOIs
    StatePublished - Aug 2002

    Keywords

    • 3-Dimensional distributions
    • Archimedean class
    • Compatibility
    • Copulas
    • Kendall's tau
    • Truncated distributions

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