## RANKS

The RANKS function computes the magnitude-based ranks of a sample population X . Elements of identical magnitude "ties" are ranked according to the mean of the ranks that would otherwise be assigned. The result is a vector of ranks equal in length to X .

This routine is written in the IDL language. Its source code can be found in the file ``` ranks.pro``` in the ``` lib``` subdirectory of the IDL distribution.

### Calling Sequence

Result = RANKS( X )

### Arguments

#### X

An n -element integer, single-, or double-precision floating-point vector. The elements of this vector must be in ascending order based on their magnitude.

### Example

Define an n -element sample population.

X = [-0.8, 0.1, -2.3, -0.6, 0.2, 1.1, -0.3, 0.6, -0.2, 1.1, \$

-0.7, -0.2, 0.6, 0.4, -0.1, 1.1, -0.3, 0.3, -1.3, 1.1]

Allocate a two-column, n -row array to store the results.

array = FLTARR(2, N_ELEMENTS(X))

Sort the sample population and store in the 0th column of ARRAY.

array[0, *] = X[SORT(X)]

Compute the ranks of the sorted sample population and store in the 1st column of ARRAY.

array[1, *] = RANKS(X[SORT(X)])

Display the sorted sample population and corresponding ranks with a two-decimal format.

PRINT, array, FORMAT = '(2(5x, f5.2))'

IDL prints:

-2.30 1.00

-1.30 2.00

-0.80 3.00

-0.70 4.00

-0.60 5.00

-0.30 6.50

-0.30 6.50

-0.20 8.50

-0.20 8.50

-0.10 10.00

0.10 11.00

0.20 12.00

0.30 13.00

0.40 14.00

0.60 15.50

0.60 15.50

1.10 18.50

1.10 18.50

1.10 18.50

1.10 18.50