Rank

2015-11-01T05:12:23Z

JHernandez2:

[[Category:Transforming functions]]
[[Category:Sorting Functions]]
[[Category:Array Functions]]
[[Category:Doc Status C]] 

Returns an array of the rank vaules of X across index I.

== Rank(x, i) ==

'''<code>Rank(x,i)</code> '''returns an array of the rank values of «x»''' '''across index «i». The lowest value in «x» has a rank value of 1, the next-lowest has a rank of 2, and so on. «i» is optional if «x» is one-dimensional. If «i» is omitted when «x» has more than one dimension, the innermost dimension is ranked. Since you, as a modeler, have little control over which dimension is the inner dimension, you should always specify «i» unless you can guarantee that «x» will always be one-dimensional.

===Advanced Variations ===

Rank(X : Array[I,keyIndex] ; I : Index ; rankType : optional ; keyIndex : Index ; descending, caseInsensitive : optional boolean[KeyIndex],
passNaNs : optional boolean )

=== Case Sensitivity ===

When ranking text values, [[Rank]] treats text values as being case-sensitive with capital letters preceding lower case letters. So, for example, "Zebra" gets a lower rank than "apply". In Analytica 4.2 or later, you can supply the optional parameter ''caseInsensitive:true'':
[[Rank]](D,I,caseInsensitive:true)

Case sensitivity only impacts text values.

=== Descending rank ===

You can easily reverse the rank of numeric arrays, where the largest numbers receive the lowest ranks, by simply using:
[[Rank]](-X,I)

For arrays containing text values, in Analytica 4.2 and later you can specify the optional ''descending:true'' parameter:
[[Rank]](X,I,descending:true)
which uses the reverse rank order for text as well as numbers.

=== Multi-key ranking ===

When two values are tied for the same rank, a second array can be used to break the tie. This is refered to as a multi-key sort (or multi-key rank). The first array is the primary key, the next is the secondary key, and so on. Analytica 4.2's [[Rank]] function support multi-key ranking. To use, your keys must all share a common index, ''I''. You must then introduce a new index, ''keyIndex'', to dimension your keys (any number of keys may be used), and bundle your keys into a 2-D array indexed by ''I'' and ''keyIndex''. For example, the following ranks by age, then for ties by gender:
[[Index..Do|Index]] keyIndex := ['age','gender'];
[[Rank]]( Array(keyIndex,[age,gender]), I, keyIndex )

=== Treatment of NaN and Null values ===

When a [[NaN]] value occurs in your data, [[Rank]] can either pass it through as a [[NaN]] or assign it a numeric rank. The optional ''passNaNs'' parameter controls this behavior. The special value [[NaN]] indicates an indeterminate real number, which in theory cannot be compared to other numbers, so the ordering of [[NaN]] by [[Rank]] doesn't actually make logical sense. By passing NaN values through without assigning an actual rank, you may catch errors in your model that lead to the introduction of the [[NaN]] value in the first place, since these errors continue to be propagated to your results. This is often a desirable property.

By default, [[Rank]] assigns an arbitrary ranking to [[NaN]] values -- placing them between -[[INF]] and any finite numeric value. To pass NaNs, include the optional parameter: [[Rank]](X,I,passNaNs:true)

[[Null]] values are sometimes used for missing data, and in these cases can also be passed using the passNulls:true parameter:
[[Rank]](X,I,passNulls:true).
When this is not specified, Null values are assigned a rank (with [[Null]] coming after all numeric values).

==Examples ==
In the example below, the rank of a list is evaluated. Thus, the second parameter "I" is unnecessary. A one-dimensional array is returned, indexed by "Years". This array has a value of 1 where "Year" has the smallest value, a value of 2 where "Year" has the second smallest value, and so on.

Rank(Years) →
{| border="1"
! !! colspan="5" style="text-align: left;" | Years ▶
|-
! style="width:75px;" |''' '''
! style="width:75px;" |'''2005 '''
! style="width:75px;" |'''2006 '''
! style="width:75px;" |'''2007 '''
! style="width:75px;" |'''2008 '''
! style="width:75px;" |'''2009 '''
|-
|
| 1
| 2
| 3
| 4
| 5
|}

Rank(Car_prices, Car_type) →

{| class="wikitable"
!
! 2005
! 2007
! 2007
! 2008
! 2009
|-
! VW
| 1 || 1 || 1 || 1 || 1
|-
! Honda
| 2 || 2 || 2 || 2 || 2
|-
! BMW
| 3 || 3 || 3 || 3 || 3
|}

===Optional Type Parameter Example:===

Index RankType := [-1,0,1, Null]

Rank(NumRepairs,CarNum,Type:RankType →

{| class="wikitable"
!
! 1
! 2
! 3
! 4
! 5
! 6
! 7
|-
! -1
| 7 || 2 || 6 || 2 || 2 || 1 || 2
|-
! 0
| 7 || 3.5 || 6 || 3.5 || 3.5 || 1 || 3.5
|-
! 1
| 7 || 5 || 6 || 5 || 5 || 1 || 5
|-
! Null
| 7 || 2 || 6 || 3|| 4 || 1 || 5
|}

===Multi-Key Example:===
Rank(NumMaintEvents,CarNum,KeyIndex:MaintType) → CarNum →

{| class="wikitable"
!
! 1
! 2
! 3
! 4
! 5
! 6
! 7
|-
!
| 7 || 4 || 6 || 2 || 3 || 1 || 5
|}

See [[Example variables]] for example array variables used here and below.

==Optional Parameters==

===Type===

If two (or N) values are equal, they receive the same rank and the next higher value receives a rank 2 (or N) higher. You can use an optional parameter, '''Type''', to control which rank is assigned to equal values. By default, the lowest rank is used, equivalent to '''Rank(x,i,Type:-1)'''. Alternatively, '''Rank(x,i,Type:0)''' uses the mid-rank and '''Rank(x,i,Type:1)''' uses the upper-rank. '''Rank(x,i,Type:Null)''' assigns a unique rank to every element (the numbers 1 thru N) in which tied elements may have different ranks.

===keyIndex===

A multi-key rank can be processed by indexing each key with a new index, and specifying this index for the optional '''keyIndex''' parameter. In a multi-key rank, '''x[@KeyIndex=1]''' determines the rank order, except that ties are then resolved using '''x[@KeyIndex=2]''', any ties there are resolved using '''x[@KeyIndex=3]''', and so on.

===descending===

'''Rank(x,i,descending:true)''' assigns the largest value a rank 1, the second largest a rank 2, and so on.

===caseInsensitive===

When x contains textual values, the optional boolean parameter '''caseInsensitive''':true ignores upper-lower case differences during the comparisons. The parameters '''descending''' and '''caseInsensitive''' may also be indexed by the keyIndex when they vary by key.

===passNaNs, passNulls===

By default, ''Rank'' assigns an arbitrary ranking to '''NaN''' or '''Null''' values. Alternatively, you can pass these through to the result as '''NaN''' or '''Null''' using '''Rank(x,i,passNaNs:true, passNulls:true)'''.

==History==

===New to 4.0===

The rank type determines how values in X that occur multiple times are ranked. For example, if the value x=5 occurs 6 times, and there are 3 other values in X that are less than 5, then x=5 appears in the sort-order at positions 4,5,6,7,8, and 9. The lower-rank of x=5 is 4, the upper-rank of x=5 is 9, and the mid-rank is 6.5. Note that a mid-rank is not necessary a valid index position (since it may be fractional), so if you intend to use the result of Rank in a slice function, you should use either the lower-rank (the default) or the upper-rank.

===New to 4.2===

When you want every element to be assigned a unique rank, you can specify ''rankType:null''. Tied elements will be given unique ranks (with their position in the original array being used to break the tie).

The [[RankCorrel]] function also allows you to select which rank type to use, but it uses mid-rank by default in Analytica 4.0.

==See Also ==

* [[Sort]]
* [[SortIndex]]
* [[RankCorrel]]
* [[Examples variables]]

Rank

2015-11-01T04:44:19Z

JHernandez2:

[[Category:Transforming functions]]
[[Category:Sorting Functions]]
[[Category:Array Functions]]
[[Category:Doc Status C]] 

Returns an array of the rank vaules of X across index I.

== Rank(x, i) ==

The lowest value in <tt>x</tt> has a rank value of 1, the next-lowest has a rank of 2, and so on. <tt>i</tt> is optional if <tt>x</tt> is one-dimensional. If <tt>i</tt> is omitted when <tt>x</tt> has more than one dimension, the innermost dimension is ranked. Since you, as a modeler, have little control over which dimension is the inner dimension, you should always specify <tt>i</tt> unless you can guarantee that <tt>x</tt>will always be one-dimensional.

===Advanced Variations ===

Rank(X : Array[I,keyIndex] ; I : Index ; rankType : optional ; keyIndex : Index ; descending, caseInsensitive : optional boolean[KeyIndex],
passNaNs : optional boolean )

=== Case Sensitivity ===

When ranking text values, [[Rank]] treats text values as being case-sensitive with capital letters preceding lower case letters. So, for example, "Zebra" gets a lower rank than "apply". In Analytica 4.2 or later, you can supply the optional parameter ''caseInsensitive:true'':
[[Rank]](D,I,caseInsensitive:true)

Case sensitivity only impacts text values.

=== Descending rank ===

You can easily reverse the rank of numeric arrays, where the largest numbers receive the lowest ranks, by simply using:
[[Rank]](-X,I)

For arrays containing text values, in Analytica 4.2 and later you can specify the optional ''descending:true'' parameter:
[[Rank]](X,I,descending:true)
which uses the reverse rank order for text as well as numbers.

=== Multi-key ranking ===

When two values are tied for the same rank, a second array can be used to break the tie. This is refered to as a multi-key sort (or multi-key rank). The first array is the primary key, the next is the secondary key, and so on. Analytica 4.2's [[Rank]] function support multi-key ranking. To use, your keys must all share a common index, ''I''. You must then introduce a new index, ''keyIndex'', to dimension your keys (any number of keys may be used), and bundle your keys into a 2-D array indexed by ''I'' and ''keyIndex''. For example, the following ranks by age, then for ties by gender:
[[Index..Do|Index]] keyIndex := ['age','gender'];
[[Rank]]( Array(keyIndex,[age,gender]), I, keyIndex )

=== Treatment of NaN and Null values ===

When a [[NaN]] value occurs in your data, [[Rank]] can either pass it through as a [[NaN]] or assign it a numeric rank. The optional ''passNaNs'' parameter controls this behavior. The special value [[NaN]] indicates an indeterminate real number, which in theory cannot be compared to other numbers, so the ordering of [[NaN]] by [[Rank]] doesn't actually make logical sense. By passing NaN values through without assigning an actual rank, you may catch errors in your model that lead to the introduction of the [[NaN]] value in the first place, since these errors continue to be propagated to your results. This is often a desirable property.

By default, [[Rank]] assigns an arbitrary ranking to [[NaN]] values -- placing them between -[[INF]] and any finite numeric value. To pass NaNs, include the optional parameter: [[Rank]](X,I,passNaNs:true)

[[Null]] values are sometimes used for missing data, and in these cases can also be passed using the passNulls:true parameter:
[[Rank]](X,I,passNulls:true).
When this is not specified, Null values are assigned a rank (with [[Null]] coming after all numeric values).

==Examples ==

===Basic Example===

Rank(Years) →
{| border="1"
! !! colspan="5" style="text-align: left;" | Years ▶
|-
! style="width:75px;" |''' '''
! style="width:75px;" |'''2005 '''
! style="width:75px;" |'''2006 '''
! style="width:75px;" |'''2007 '''
! style="width:75px;" |'''2008 '''
! style="width:75px;" |'''2009 '''
|-
|
| 1
| 2
| 3
| 4
| 5
|}

Rank(Car_prices, Car_type) → Car_type ↓ , Years →

{| class="wikitable"
!
! 2005
! 2007
! 2007
! 2008
! 2009
|-
! VW
| 1 || 1 || 1 || 1 || 1
|-
! Honda
| 2 || 2 || 2 || 2 || 2
|-
! BMW
| 3 || 3 || 3 || 3 || 3
|}

===Optional Type Parameter Example:===

Index RankType := [-1,0,1, Null]

Rank(NumRepairs,CarNum,Type:RankType → Rank_type ↓ , CarNum →

{| class="wikitable"
!
! 1
! 2
! 3
! 4
! 5
! 6
! 7
|-
! -1
| 7 || 2 || 6 || 2 || 2 || 1 || 2
|-
! 0
| 7 || 3.5 || 6 || 3.5 || 3.5 || 1 || 3.5
|-
! 1
| 7 || 5 || 6 || 5 || 5 || 1 || 5
|-
! Null
| 7 || 2 || 6 || 3|| 4 || 1 || 5
|}

===Multi-Key Example:===
Rank(NumMaintEvents,CarNum,KeyIndex:MaintType) → CarNum →

{| class="wikitable"
!
! 1
! 2
! 3
! 4
! 5
! 6
! 7
|-
!
| 7 || 4 || 6 || 2 || 3 || 1 || 5
|}

See [[Example variables]] for example array variables used here and below.

==Optional Parameters==

===Type===

If two (or N) values are equal, they receive the same rank and the next higher value receives a rank 2 (or N) higher. You can use an optional parameter, '''Type''', to control which rank is assigned to equal values. By default, the lowest rank is used, equivalent to '''Rank(x,i,Type:-1)'''. Alternatively, '''Rank(x,i,Type:0)''' uses the mid-rank and '''Rank(x,i,Type:1)''' uses the upper-rank. '''Rank(x,i,Type:Null)''' assigns a unique rank to every element (the numbers 1 thru N) in which tied elements may have different ranks.

===keyIndex===

A multi-key rank can be processed by indexing each key with a new index, and specifying this index for the optional '''keyIndex''' parameter. In a multi-key rank, '''x[@KeyIndex=1]''' determines the rank order, except that ties are then resolved using '''x[@KeyIndex=2]''', any ties there are resolved using '''x[@KeyIndex=3]''', and so on.

===descending===

'''Rank(x,i,descending:true)''' assigns the largest value a rank 1, the second largest a rank 2, and so on.

===caseInsensitive===

When x contains textual values, the optional boolean parameter '''caseInsensitive''':true ignores upper-lower case differences during the comparisons. The parameters '''descending''' and '''caseInsensitive''' may also be indexed by the keyIndex when they vary by key.

===passNaNs, passNulls===

By default, ''Rank'' assigns an arbitrary ranking to '''NaN''' or '''Null''' values. Alternatively, you can pass these through to the result as '''NaN''' or '''Null''' using '''Rank(x,i,passNaNs:true, passNulls:true)'''.

==History==

===New to 4.0===

The rank type determines how values in X that occur multiple times are ranked. For example, if the value x=5 occurs 6 times, and there are 3 other values in X that are less than 5, then x=5 appears in the sort-order at positions 4,5,6,7,8, and 9. The lower-rank of x=5 is 4, the upper-rank of x=5 is 9, and the mid-rank is 6.5. Note that a mid-rank is not necessary a valid index position (since it may be fractional), so if you intend to use the result of Rank in a slice function, you should use either the lower-rank (the default) or the upper-rank.

===New to 4.2===

When you want every element to be assigned a unique rank, you can specify ''rankType:null''. Tied elements will be given unique ranks (with their position in the original array being used to break the tie).

The [[RankCorrel]] function also allows you to select which rank type to use, but it uses mid-rank by default in Analytica 4.0.

==See Also ==

* [[Sort]]
* [[SortIndex]]
* [[RankCorrel]]
* [[Example variables]]

Rank

2015-11-01T04:41:36Z

JHernandez2:

[[Category:Transforming functions]]
[[Category:Sorting Functions]]
[[Category:Array Functions]]
[[Category:Doc Status C]] 

Returns an array of the rank vaules of X across index I.

== Rank(x, i) ==

The lowest value in <tt>x</tt> has a rank value of 1, the next-lowest has a rank of 2, and so on. <tt>i</tt> is optional if <tt>x</tt> is one-dimensional. If <tt>i</tt> is omitted when <tt>x</tt> has more than one dimension, the innermost dimension is ranked. Since you, as a modeler, have little control over which dimension is the inner dimension, you should always specify <tt>i</tt> unless you can guarantee that <tt>x</tt>will always be one-dimensional.

===Advanced Variations ===

Rank(X : Array[I,keyIndex] ; I : Index ; rankType : optional ; keyIndex : Index ; descending, caseInsensitive : optional boolean[KeyIndex],
passNaNs : optional boolean )

=== Case Sensitivity ===

When ranking text values, [[Rank]] treats text values as being case-sensitive with capital letters preceding lower case letters. So, for example, "Zebra" gets a lower rank than "apply". In Analytica 4.2 or later, you can supply the optional parameter ''caseInsensitive:true'':
[[Rank]](D,I,caseInsensitive:true)

Case sensitivity only impacts text values.

=== Descending rank ===

You can easily reverse the rank of numeric arrays, where the largest numbers receive the lowest ranks, by simply using:
[[Rank]](-X,I)

For arrays containing text values, in Analytica 4.2 and later you can specify the optional ''descending:true'' parameter:
[[Rank]](X,I,descending:true)
which uses the reverse rank order for text as well as numbers.

=== Multi-key ranking ===

When two values are tied for the same rank, a second array can be used to break the tie. This is refered to as a multi-key sort (or multi-key rank). The first array is the primary key, the next is the secondary key, and so on. Analytica 4.2's [[Rank]] function support multi-key ranking. To use, your keys must all share a common index, ''I''. You must then introduce a new index, ''keyIndex'', to dimension your keys (any number of keys may be used), and bundle your keys into a 2-D array indexed by ''I'' and ''keyIndex''. For example, the following ranks by age, then for ties by gender:
[[Index..Do|Index]] keyIndex := ['age','gender'];
[[Rank]]( Array(keyIndex,[age,gender]), I, keyIndex )

=== Treatment of NaN and Null values ===

When a [[NaN]] value occurs in your data, [[Rank]] can either pass it through as a [[NaN]] or assign it a numeric rank. The optional ''passNaNs'' parameter controls this behavior. The special value [[NaN]] indicates an indeterminate real number, which in theory cannot be compared to other numbers, so the ordering of [[NaN]] by [[Rank]] doesn't actually make logical sense. By passing NaN values through without assigning an actual rank, you may catch errors in your model that lead to the introduction of the [[NaN]] value in the first place, since these errors continue to be propagated to your results. This is often a desirable property.

By default, [[Rank]] assigns an arbitrary ranking to [[NaN]] values -- placing them between -[[INF]] and any finite numeric value. To pass NaNs, include the optional parameter: [[Rank]](X,I,passNaNs:true)

[[Null]] values are sometimes used for missing data, and in these cases can also be passed using the passNulls:true parameter:
[[Rank]](X,I,passNulls:true).
When this is not specified, Null values are assigned a rank (with [[Null]] coming after all numeric values).

==Examples ==

===Basic Example===

Rank(Years) →

<code>Variable Rate_of_inflation :=</code>
{| border="1"
! !! colspan="5" style="text-align: left;" | Years ▶
|-
! style="width:75px;" |''' '''
! style="width:75px;" |'''2005 '''
! style="width:75px;" |'''2006 '''
! style="width:75px;" |'''2007 '''
! style="width:75px;" |'''2008 '''
! style="width:75px;" |'''2009 '''
|-
|
| 1
| 2
| 3
| 4
| 5
|}

Rank(Car_prices, Car_type) → Car_type ↓ , Years →

{| class="wikitable"
!
! 2005
! 2007
! 2007
! 2008
! 2009
|-
! VW
| 1 || 1 || 1 || 1 || 1
|-
! Honda
| 2 || 2 || 2 || 2 || 2
|-
! BMW
| 3 || 3 || 3 || 3 || 3
|}

===Optional Type Parameter Example:===

Index RankType := [-1,0,1, Null]

Rank(NumRepairs,CarNum,Type:RankType → Rank_type ↓ , CarNum →

{| class="wikitable"
!
! 1
! 2
! 3
! 4
! 5
! 6
! 7
|-
! -1
| 7 || 2 || 6 || 2 || 2 || 1 || 2
|-
! 0
| 7 || 3.5 || 6 || 3.5 || 3.5 || 1 || 3.5
|-
! 1
| 7 || 5 || 6 || 5 || 5 || 1 || 5
|-
! Null
| 7 || 2 || 6 || 3|| 4 || 1 || 5
|}

===Multi-Key Example:===
Rank(NumMaintEvents,CarNum,KeyIndex:MaintType) → CarNum →

{| class="wikitable"
!
! 1
! 2
! 3
! 4
! 5
! 6
! 7
|-
!
| 7 || 4 || 6 || 2 || 3 || 1 || 5
|}

See [[Example variables]] for example array variables used here and below.

==Optional Parameters==

===Type===

If two (or N) values are equal, they receive the same rank and the next higher value receives a rank 2 (or N) higher. You can use an optional parameter, '''Type''', to control which rank is assigned to equal values. By default, the lowest rank is used, equivalent to '''Rank(x,i,Type:-1)'''. Alternatively, '''Rank(x,i,Type:0)''' uses the mid-rank and '''Rank(x,i,Type:1)''' uses the upper-rank. '''Rank(x,i,Type:Null)''' assigns a unique rank to every element (the numbers 1 thru N) in which tied elements may have different ranks.

===keyIndex===

A multi-key rank can be processed by indexing each key with a new index, and specifying this index for the optional '''keyIndex''' parameter. In a multi-key rank, '''x[@KeyIndex=1]''' determines the rank order, except that ties are then resolved using '''x[@KeyIndex=2]''', any ties there are resolved using '''x[@KeyIndex=3]''', and so on.

===descending===

'''Rank(x,i,descending:true)''' assigns the largest value a rank 1, the second largest a rank 2, and so on.

===caseInsensitive===

When x contains textual values, the optional boolean parameter '''caseInsensitive''':true ignores upper-lower case differences during the comparisons. The parameters '''descending''' and '''caseInsensitive''' may also be indexed by the keyIndex when they vary by key.

===passNaNs, passNulls===

By default, ''Rank'' assigns an arbitrary ranking to '''NaN''' or '''Null''' values. Alternatively, you can pass these through to the result as '''NaN''' or '''Null''' using '''Rank(x,i,passNaNs:true, passNulls:true)'''.

==History==

===New to 4.0===

The rank type determines how values in X that occur multiple times are ranked. For example, if the value x=5 occurs 6 times, and there are 3 other values in X that are less than 5, then x=5 appears in the sort-order at positions 4,5,6,7,8, and 9. The lower-rank of x=5 is 4, the upper-rank of x=5 is 9, and the mid-rank is 6.5. Note that a mid-rank is not necessary a valid index position (since it may be fractional), so if you intend to use the result of Rank in a slice function, you should use either the lower-rank (the default) or the upper-rank.

===New to 4.2===

When you want every element to be assigned a unique rank, you can specify ''rankType:null''. Tied elements will be given unique ranks (with their position in the original array being used to break the tie).

The [[RankCorrel]] function also allows you to select which rank type to use, but it uses mid-rank by default in Analytica 4.0.

==See Also ==

* [[Sort]]
* [[SortIndex]]
* [[RankCorrel]]
* [[Example variables]]

Uncumulate

2015-11-01T04:19:45Z

JHernandez2: /* See Also */

Uncumulate

2015-11-01T04:18:13Z

JHernandez2: