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A counterexample to a conjecture of Hutchinson and Lai. (Un contre-exemple à une conjecture de Hutchinson et Lai.) (French. Abridged English version) Zbl 1194.60022

Summary: In 1990, T. P. Hutchinson and C. D. Lai [Continuous bivariate distributions, emphasising applications. Adelaide: Rumsby Scientific Publishing (1990; Zbl 1170.62330)] conjectured that if a random pair \((X,Y)\) is stochastically increasing in \(X\) and \(Y\), then Spearman’s rho and Kendall’s tau are such that \(1 + 3 \tau \leqslant (\rho +1)^{2}\). This conjecture is disproved.

MSC:

60E15 Inequalities; stochastic orderings

Citations:

Zbl 1170.62330
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References:

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