Dependence of non-continuous random variables
Dependence of non-continuous random variables
Dependence of non-continuous random variables
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Fallacies <strong>Dependence</strong> Concordance Measures Problems & References AppendixTowards Kendall’s Tau and Spearman’s RhoDifference between the probabilities <strong>of</strong> concordance anddiscordance equals 4 ∫ C S (u,v)dC S ∗ (u,v) − 1Consider• Kendall’s tau: ˜τ(C S ) = 4• Spearman’s rho: ˜ρ(C S ) = 12However∫ 1 ∫ 100∫ 1 ∫ 1• ˜τ and ˜ρ do not reach the bounds 1 and −10C S (u,v) dC S (u,v) − 10[C S (u,v) − uv] du dv• Exact bounds <strong>of</strong> ˜τ and ˜ρ are complicated and do not have thesame absolute valueJ. Nešlehová ETH Zurich<strong>Dependence</strong> <strong>of</strong> <strong>non</strong>-<strong>continuous</strong> <strong>random</strong> <strong>variables</strong>
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