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The TP2 ordering of Kimeldorf and Sampson has the normal-agreeing property

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  • Genest, Christian
  • Verret, François
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    Abstract

    Kimeldorf and Sampson (Ann. Inst. Statist. Math. 39 (1987) 113) proposed a positive dependence ordering that extends the TP2 concept of dependence defined for bivariate distributions by Block et al. (Ann. Probab. 10 (1982) 765). It is shown here that in this ordering, the bivariate normal distributions with given means and variances are ordered by their correlation coefficient. It is also pointed out that except possibly for the Ali-Mikhail-Haq and Gumbel-Barnett families, none of the common classes of Archimedean copulas meets the TP2 condition of Kimeldorf and Sampson.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 57 (2002)
    Issue (Month): 4 (May)
    Pages: 387-391

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    Handle: RePEc:eee:stapro:v:57:y:2002:i:4:p:387-391

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    Related research

    Keywords: Copula Positive quadrant dependence Total positivity of order two TP2 ordering;

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    Cited by:
    1. Rinott, Yosef & Scarsini, Marco, 2006. "Total positivity order and the normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1251-1261, May.

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