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Positive dependence properties of elliptically symmetric distributions

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  • Sampson, Allan R.

Abstract

Let X1, ..., Xp have p.d.f. g(x12 + ... + xp2). It is shown that (a) X1, ..., Xp are positively lower orthant dependent or positively upper orthant dependent if, and only if, X1,..., Xp are i.i.d. N(0, [sigma]2); and (b) the p.d.f. of X1,..., Xp is TP2 in pairs if, and only if, In g(u) is convex. Let X1, X2 have p.d.f. f(x1, x2) = [Sigma]-1/2 g((x1, x2) [Sigma]-1(x1, x2)'). Necessary and sufficient conditions are given for f(x1, x2) to be TP2 for fixed correlation [varrho]. It is shown that if f is TP2 for all [varrho] >0. then (X1, X2)' ~ N(0, [Sigma]). Related positive dependence results and applications are also considered.

Suggested Citation

  • Sampson, Allan R., 1983. "Positive dependence properties of elliptically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 375-381, June.
    • Handle: RePEc:eee:jmvana:v:13:y:1983:i:2:p:375-381
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    Cited by:

    1. Kurowicka, Dorota & van Horssen, Wim T., 2015. "On an interaction function for copulas," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 127-142.
    2. Block, Henry W. & Savits, Thomas H. & Wang, Jie & Sarkar, Sanat K., 2013. "The multivariate-t distribution and the Simes inequality," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 227-232.
    3. Kundu, Debasis & Balakrishnan, N. & Jamalizadeh, Ahad, 2013. "Generalized multivariate Birnbaum–Saunders distributions and related inferential issues," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 230-244.

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