Concordant pair

In statistics, a  concordant pair is a pair of a two-variable (bivariate) observation data-set {X1,Y1} and {X2,Y2}, where:


 * $$ \sgn (X_2 - X_1)\ = \sgn (Y_2 - Y_1)\ $$

Correspondingly, a  discordant pair is a pair, as defined above, where


 * $$ \sgn (X_2 - X_1)\ = - \sgn (Y_2 - Y_1)\ $$

and the sign function, often represented as sgn, is defined as:


 * $$ \sgn x = \left\{ \begin{matrix}

-1 & : & x < 0 \\ 0 & : & x = 0 \\ 1 & : & x > 0 \end{matrix} \right. $$