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@kevmal
kevmal committed Apr 28, 2024
1 parent 87a2717 commit 8c2a8e5
Showing 1 changed file with 48 additions and 32 deletions.
80 changes: 48 additions & 32 deletions src/FSharp.Stats/Correlation.fs
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Expand Up @@ -302,8 +302,7 @@ module Correlation =
/// <param name="n1">sum_i(t_i(t_i-1)/2) where t_is is t_i he number of pairs of observations with the same x value.</param>
/// <param name="n2">sum_i(u_i(u_i-1)/2) where u_is is u_i he number of pairs of observations with the same y value.</param>
/// <returns>The Kendall tau A statistic.</returns>
let tauA _x _y pq n0 _n1 _n2 =
pq / float n0
let tauA _x _y pq n0 _n1 _n2 = pq / float n0
/// <summary>
/// Tau B - Adjust for ties. tau_b = pq / sqrt((n0 - n1)(n0 - n2))
/// </summary>
Expand Down Expand Up @@ -342,13 +341,15 @@ module Correlation =
/// It is a measure of rank correlation: the similarity of the orderings of the data when ranked by each of the quantities.
/// </remarks>
/// <param name="tau">
/// The Kendall tau function to use. x: 'a[] -> y: 'b[] -> pq: float -> n0: int -> n1: int -> n2: int -> 'c
/// - x: The first array of observations.
/// - y: The second array of observations.
/// - pq: Number of concordant minues the number of discordant pairs.
/// - n0: he number of pairs of observations.
/// - n1: sum_i(t_i(t_i-1)/2) where t_is is t_i he number of pairs of observations with the same x value.
/// - n2: sum_i(u_i(u_i-1)/2) where u_is is u_i he number of pairs of observations with the same y value.
/// The Kendall tau function to use. x: 'a[] -> y: 'b[] -> pq: float -> n0: int -> n1: int -> n2: int -> 'c
/// <list>
/// <item><term>x: </term><description>The first array of observations.</description></item>
/// <item><term>y: </term><description>The second array of observations.</description></item>
/// <item><term>pq: </term><description>Number of concordant minues the number of discordant pairs.</description></item>
/// <item><term>n0: </term><description>The number of pairs of observations.</description></item>
/// <item><term>n1: </term><description>sum_i(t_i(t_i-1)/2) where t_is is t_i he number of pairs of observations with the same x value.</description></item>
/// <item><term>n2: </term><description>sum_i(u_i(u_i-1)/2) where u_is is u_i he number of pairs of observations with the same y value.</description></item>
/// </list>
/// The function would generally return the Kendall tau statistic, however, this setup to allow for returning other values, p-values, multiple statistics, etc.
/// </param>
/// <param name="x"> The first sequence of observations. </param>
Expand Down Expand Up @@ -422,15 +423,17 @@ module Correlation =
tau x y pq n0 n1 n2

/// <summary>Kendall Correlation Coefficient</summary>
/// <remarks>Computes Kendall Tau-A rank correlation coefficient between two sequences of observations. No adjustment is made for ties.
/// tau_a = (n_c - n_d) / n_0 where
/// n_c is the number of concordant pairs,
/// n_d is the number of discordant pairs, and
/// n_0 = n*(n-1)/2 where n is the number of observations.
/// <remarks>Computes Kendall Tau-a rank correlation coefficient between two sequences of observations. No adjustment is made for ties.
/// tau_a = (n_c - n_d) / n_0, where
/// <list>
/// <item><term>n_c: </term><description>Number of concordant pairs.</description></item>
/// <item><term>n_d: </term><description>Number of discordant pairs.</description></item>
/// <item><term>n_0: </term><description>n*(n-1)/2 where n is the number of observations.</description></item>
/// </list>
/// </remarks>
/// <param name="seq1">The first sequence of observations.</param>
/// <param name="seq2">The second sequence of observations.</param>
/// <returns>Kendall rank correlation coefficient of setA and setB</returns>
/// <returns>Kendall Tau-a rank correlation coefficient of setA and setB</returns>
/// <example>
/// <code>
/// let x = [5.05;6.75;3.21;2.66]
Expand All @@ -445,17 +448,19 @@ module Correlation =
kendallTau Kendall.tauA setA setB

/// <summary>Kendall Correlation Coefficient</summary>
/// <remarks>Computes Kendall Tau-B rank correlation coefficient between two sequences of observations. Tau-b is used to adjust for ties.
/// tau_b = (n_c - n_d) / sqrt((n_0 - n_1) * (n_0 - n_2)) where
/// n_c is number of concordant pairs,
/// n_d is number of discordant pairs,
/// n_0 = n*(n-1)/2 where n is the number of observations,
/// n_1 = sum_i(t_i(t_i-1)/2) where t_i is the number of pairs of observations with the same x value,
/// n_2 = sum_i(u_i(u_i-1)/2) where u_i is the number of pairs of observations with the same y value.
/// <remarks>Computes Kendall Tau-b rank correlation coefficient between two sequences of observations. Tau-b is used to adjust for ties.
/// tau_b = (n_c - n_d) / sqrt((n_0 - n_1) * (n_0 - n_2)), where
/// <list>
/// <item><term>n_c: </term><description>Number of concordant pairs.</description></item>
/// <item><term>n_d: </term><description>Number of discordant pairs.</description></item>
/// <item><term>n_0: </term><description>n*(n-1)/2 where n is the number of observations.</description></item>
/// <item><term>n_1: </term><description>sum_i(t_i(t_i-1)/2) where t_i is the number of pairs of observations with the same x value.</description></item>
/// <item><term>n_2: </term><description>sum_i(u_i(u_i-1)/2) where u_i is the number of pairs of observations with the same y value.</description></item>
/// </list>
/// </remarks>
/// <param name="seq1">The first sequence of observations.</param>
/// <param name="seq2">The second sequence of observations.</param>
/// <returns>Kendall Tau-B rank correlation coefficient of setA and setB</returns>
/// <returns>Kendall Tau-b rank correlation coefficient of seq1 and seq2</returns>
/// <example>
/// <code>
/// let x = [5.05;6.75;3.21;2.66]
Expand All @@ -470,16 +475,18 @@ module Correlation =
kendallTau Kendall.tauB setA setB

/// <summary>Kendall Correlation Coefficient</summary>
/// <remarks>Computes Kendall Tau-C rank correlation coefficient between two sequences of observations. Tau-c is used to adjust for ties which is prefered to tau-b when x and y have a different number of possible values.
/// tau_c = 2(n_c - n_d) / (n^2 * (m-1)/m) where
/// n_c is number of concordant pairs,
/// n_d is number of discordant pairs,
/// n is the number of observations,
/// m = min(distinct x, distinct y).
/// <remarks>Computes Kendall Tau-c rank correlation coefficient between two sequences of observations. Tau-c is used to adjust for ties which is preferred to Tau-b when x and y have a different number of possible values.
/// tau_c = 2(n_c - n_d) / (n^2 * (m-1)/m), where
/// <list>
/// <item><term>n_c: </term><description>Number of concordant pairs.</description></item>
/// <item><term>n_d: </term><description>Number of discordant pairs.</description></item>
/// <item><term>n: </term><description>The number of observations.</description></item>
/// <item><term>m: </term><description>The lesser of the distinct x count and distinct y count.</description></item>
/// </list>
/// </remarks>
/// <param name="seq1">The first sequence of observations.</param>
/// <param name="seq2">The second sequence of observations.</param>
/// <returns>Kendall Tau-C rank correlation coefficient of setA and setB</returns>
/// <returns>Kendall Tau-c rank correlation coefficient of seq1 and seq2</returns>
/// <example>
/// <code>
/// let x = [1;1;1;2;2;2;3;3;3]
Expand All @@ -495,12 +502,21 @@ module Correlation =
let setB = Array.ofSeq seq2
kendallTau Kendall.tauC setA setB


/// <summary>Kendall Correlation Coefficient</summary>
/// <remarks>Computes Kendall Tau-B rank correlation coefficient between two sequences of observations.
/// <remarks>This is an alias to <see cref="kendallTauB"/>. Computes Kendall Tau-b rank correlation coefficient between two sequences of observations. Tau-b is used to adjust for ties.
/// tau_b = (n_c - n_d) / sqrt((n_0 - n_1) * (n_0 - n_2)), where
/// <list>
/// <item><term>n_c: </term><description>Number of concordant pairs.</description></item>
/// <item><term>n_d: </term><description>Number of discordant pairs.</description></item>
/// <item><term>n_0: </term><description>n*(n-1)/2 where n is the number of observations.</description></item>
/// <item><term>n_1: </term><description>sum_i(t_i(t_i-1)/2) where t_i is the number of pairs of observations with the same x value.</description></item>
/// <item><term>n_2: </term><description>sum_i(u_i(u_i-1)/2) where u_i is the number of pairs of observations with the same y value.</description></item>
/// </list>
/// </remarks>
/// <param name="seq1">The first sequence of observations.</param>
/// <param name="seq2">The second sequence of observations.</param>
/// <returns>Kendall Tau-B rank correlation coefficient of setA and setB</returns>
/// <returns>Kendall Tau-b rank correlation coefficient of seq1 and seq2</returns>
/// <example>
/// <code>
/// let x = [5.05;6.75;3.21;2.66]
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