## BRANKS Function

**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 *x*_{j} of a vector is defined as

where

The bivariate rank of a pair (*x*_{j},*y*_{j}) is defined as

For example, the following statements
produce the result shown below:
x={1 0,
4 2,
3 4,
5 3,
6 3};
f=branks(x);
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.