Analytical proofs of classical inequalities between Spearmanʹs and Kendallʹs

Short analytical proofs are given for classical inequalities due to Daniels [1950. Rank correlation and population models. J. Roy. Statist. Soc. Ser. B 12, 171–181; 1951. Note on Durbin and Stuartʹs formula for E ( r s ) . J. Roy. Statist. Soc. Ser. B 13, 310] and Durbin and Stuart [1951. Inversions and rank correlation coefficients. J. Roy. Statist. Soc. Ser. B 13, 303–309] relating Spearmanʹs ρ and Kendallʹs τ .