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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:

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

References

Kendall rank correlation.
Kendall, M. (1948) Rank Correlation Methods, Charles Griffin & Company Limited
Kendall, M. (1938) "A New Measure of Rank Correlation", Biometrica, 30, 81-89.

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