computes bivariate ranks
- BRANKS( matrix)
where matrix is an n ×2 numeric matrix.
The BRANKS function calculates the tied ranks and
the bivariate ranks for an n ×2 matrix
and returns an n ×3 matrix of these ranks.
The tied ranks of the first column of matrix are contained
in the first column of the result matrix; the tied ranks of the
second column of matrix are contained in the second column
of the result matrix; and the bivariate ranks of matrix
are contained in the third column of the result matrix.
The tied rank of an element xj of a vector is defined as
The bivariate rank of a pair (xj,yj) is defined as
For example, the following statements
produce the result shown below:
F 5 rows 3 cols (numeric)
1 1 1
3 2 2
2 5 2
4 3.5 3
5 3.5 3.5
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.