Ranking

Summary: this tutorial demonstrates how to determine ranks of a collection

Consider a collection of values. The rank of a number is its size relative to other values in a sequence. There are four methods how to handle ties:

let mySequence = [|1.0; -2.0; 0.0; 1.0|]

• rankFirst
  • Each rank occurs exactly once. If ties are present the first occurence gets the low rank.
  • ATTENTION: If there are multiple ties (>20) the sorting of Arrays will not preserve the element order correctly!!
  • ranks = [3,1,2,4]

• rankMin
  • If ties are present all tied elements receive the score of the first occurence (min rank)

  • ranks = [3,1,2,3]

• rankMax
  • If ties are present all tied elements receive the score of the last occurence (max rank)
  • ranks = [4,1,2,4]

• rankAverge
  • If ties are present all tied elements receive their average rank.
  • ranks = [3.5,1,2,3.5]

NaN treatment

If nans are present in the collection, there are several ways to treat them. In general nan <> nan so that each occurence will receive its unique rank. (for infinity and -infinity the equality check returns true).

• Usually nans are sorted to the beginning of the collection: nan, -infinity, -100., 0., 100, infinity
• By default in FSharp.Stats.Rank, nans are sorted to the end of the sequence (the sorting can be defined as optional parameter)
• Additionally ranks of nan values are set to nan if not specified othwerwise

open FSharp.Stats

let collection = [|2.;-infinity;infinity;infinity;nan;0|]

Rank.RankFirst() collection
// result:  [|3.0; 1.0; 4.0; 5.0; nan; 2.0|]

Rank.RankMin() collection
// result:  [|3.0; 1.0; 4.0; 4.0; nan; 2.0|]

Rank.RankMax() collection
// result:  [|3.0; 1.0; 5.0; 5.0; nan; 2.0|]

Rank.RankAverage() collection
// result:  [|3.0; 1.0; 4.5; 4.5; nan; 2.0|]

If you want to preserve the true ranks of nans but sort them to the back you can use:

Rank.RankFirst(RankNanWithNan=false) collection
// result:  [|3.0; 1.0; 4.0; 5.0; 6.0; 2.0|]

If you want to preserve the true ranks of nans AND sort them to the beginning you can use:

Rank.RankFirst(NanIsMaximum=false,RankNanWithNan=false) collection
// result:  [|4.0; 2.0; 5.0; 6.0; 1.0; 3.0|]