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Statistics

  

Rank

  

rank data items according to their numeric values

 

Calling Sequence

Parameters

Description

Options

Notes

Examples

Calling Sequence

Rank(X, options)

Parameters

X

-

data sample

options

-

(optional) equation(s) of the form option=value where option is one of order or output; specify options for the Rank function

Description

• 

For a data set X of size n, the Rank command ranks the elements of X according to their floating-point values.

• 

By default, an array of ranks is returned, that is an array of distinct integers between 1 and n. By default the elements of X are ranks in the ascending order. Note that if i is different from j then datai and dataj will receive distinct ranks even if data[i] = data[j].

• 

The first parameter X is the data set - given as e.g. a Vector.

Options

  

The options argument can contain one or more of the options shown below.

• 

order=ascending or descending -- Indicate whether the elements of X should be ranked in the ascending or descending order. The default value is order=ascending.

• 

output=table -- By default (output=rtable) different elements of X receive different ranks even if the two elements have the same numeric value. If this option is set to output=table then the elements of X will be ranked according to their position in the sorted sample with all multiple occurrences removed.

Notes

• 

Each element of X can be any Maple expression, but this expression must be able to be evaluated to a floating-point number. Failure to evaluate to do so will generate an exception.

• 

If the output option is set to output=table all elements in X must be of type numeric.

• 

The Rank command leaves the original data set X unchanged.

Examples

withStatistics:

AArray0.5,0.7,0.5,0.1,0.3,0.1,0.2,0.1

A:=0.50.70.50.10.30.10.20.1

(1)

Rank the elements of A in the ascending order.

RRankA

R:=68715243

(2)

Reorder the elements of A according to their ranks.

BOrderByRankA,R

B:=0.10.10.10.20.30.50.50.7

(3)

Reorder the elements of A in the descending order.

QRankA,order=descending

Q:=21364758

(4)

COrderByRankA,Q

C:=0.70.50.50.30.20.10.10.1

(5)

Build the ranks table.

TRankA,output=table

T:=table0.7=5,0.1=1,0.3=3,0.2=2,0.5=4

(6)

A4,TA4

0.1,1

(7)

A1,TA1

0.5,4

(8)

See Also

Statistics

Statistics[Computation]

Statistics[Sort]

 


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