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Geometric mean of two copulas

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(a) Let C0 and C1 be copulas, and let q be any number in I. Show that the weighted arithmetic mean ( ) 1- + q q C C 0 1 is also a copula. Hence conclude that any convex linear combination of copulas is a copula.

(b) Show that the geometric mean of two copulas may fail to be a copula. [Hint: Let C be the geometric mean of P and W, and show that the C-volume of the rectangle [ ] 1234 , ¥[ ] 1234 , is negative.]

Reference no: EM133198474

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