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@@ -0,0 +1,132 @@
+
+
+
+![]() |
+Home | +Libraries | +People | +FAQ | +More | +
#include <boost/math/statistics/chatterjee_correlation.hpp> + +namespace boost::math::statistics { + + C++17: + template <typename ExecutionPolicy, typename Container> + auto chatterjee_correlation(ExecutionPolicy&& exec, const Container& u, const Container& v); + + C++11: + template <typename Container> + auto chatterjee_correlation(const Container& u, const Container& v); +} ++
+ The classical correlation coefficients like the Pearson's correlation are useful + primarily for distinguishing when one dataset depends linearly on another. + However, Pearson's correlation coefficient has a known weakness in that when + the dependent variable has an obvious functional relationship with the independent + variable, the value of the correlation coefficient can take on any value. As + Chatterjee says: +
++ > Ideally, one would like a coefficient that approaches its maximum value + if and only if one variable looks more and more like a noiseless function of + the other, just as Pearson correlation is close to its maximum value if and + only if one variable is close to being a noiseless linear function of the other. +
++ This is the problem Chatterjee's coefficient solves. Let X and Y be random + variables, where Y is not constant, and let (X_i, Y_i) be samples from this + distribution. Rearrange these samples so that X_(0) < X_{(1)} < ... X_{(n-1)} + and create (R(X_{(i)}), R(Y_{(i)})). The Chatterjee correlation is then given + by +
++ +
++ In the limit of an infinite amount of i.i.d data, the statistic lies in [0, + 1]. However, if the data is not infinite, the statistic may be negative. If + X and Y are independent, the value is zero, and if Y is a measurable function + of X, then the statistic is unity. The complexity is O(n log n). +
++ An example is given below: +
+std::vector<double> X{1,2,3,4,5}; +std::vector<double> Y{1,2,3,4,5}; +using boost::math::statistics::chatterjee_correlation; +double coeff = chatterjee_correlation(X, Y); ++
+ The implementation follows Chatterjee's + paper. +
++ Nota bene: If the input is an integer type the output + will be a double precision type. +
++ The function expects at least two samples, a non-constant vector Y, and the + same number of X's as Y's. If Y is constant, the result is a quiet NaN. The + data set must be sorted by X values. If there are ties in the values of X, + then the statistic is random due to the random breaking of ties. Of course, + random numbers are not used internally, but the result is not guaranteed to + be identical on different systems. +
+| - | - |



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diff --git a/doc/html/math_toolkit/credits.html b/doc/html/math_toolkit/credits.html
index f33f50643..7070d31ab 100644
--- a/doc/html/math_toolkit/credits.html
+++ b/doc/html/math_toolkit/credits.html
@@ -4,10 +4,11 @@
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diff --git a/doc/html/math_toolkit/cubic_hermite.html b/doc/html/math_toolkit/cubic_hermite.html
index ff2bcfeab..1e4da4d42 100644
--- a/doc/html/math_toolkit/cubic_hermite.html
+++ b/doc/html/math_toolkit/cubic_hermite.html
@@ -4,10 +4,11 @@
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diff --git a/doc/html/math_toolkit/cubic_roots.html b/doc/html/math_toolkit/cubic_roots.html
index 38e8ced84..8de9fddc7 100644
--- a/doc/html/math_toolkit/cubic_roots.html
+++ b/doc/html/math_toolkit/cubic_roots.html
@@ -4,10 +4,11 @@
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diff --git a/doc/html/math_toolkit/daubechies.html b/doc/html/math_toolkit/daubechies.html
index 79dae5c61..d10e5be21 100644
--- a/doc/html/math_toolkit/daubechies.html
+++ b/doc/html/math_toolkit/daubechies.html
@@ -4,10 +4,11 @@
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diff --git a/doc/html/math_toolkit/daubechies_filters.html b/doc/html/math_toolkit/daubechies_filters.html
index 5fe91b291..9d9db53f0 100644
--- a/doc/html/math_toolkit/daubechies_filters.html
+++ b/doc/html/math_toolkit/daubechies_filters.html
@@ -4,10 +4,11 @@
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diff --git a/doc/html/math_toolkit/diff.html b/doc/html/math_toolkit/diff.html
index 9114719d4..4834ca13e 100644
--- a/doc/html/math_toolkit/diff.html
+++ b/doc/html/math_toolkit/diff.html
@@ -4,10 +4,11 @@
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diff --git a/doc/html/math_toolkit/diff0.html b/doc/html/math_toolkit/diff0.html
index f02ab05b6..5981deadd 100644
--- a/doc/html/math_toolkit/diff0.html
+++ b/doc/html/math_toolkit/diff0.html
@@ -4,10 +4,11 @@
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diff --git a/doc/html/math_toolkit/directories.html b/doc/html/math_toolkit/directories.html
index d4910cdcd..856c9a4f9 100644
--- a/doc/html/math_toolkit/directories.html
+++ b/doc/html/math_toolkit/directories.html
@@ -4,10 +4,11 @@
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diff --git a/doc/html/math_toolkit/dist_concept.html b/doc/html/math_toolkit/dist_concept.html
index 082ba61f6..1afc3dba1 100644
--- a/doc/html/math_toolkit/dist_concept.html
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diff --git a/doc/html/math_toolkit/dist_ref.html b/doc/html/math_toolkit/dist_ref.html
index 6cc2dfa20..361c091bd 100644
--- a/doc/html/math_toolkit/dist_ref.html
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diff --git a/doc/html/math_toolkit/dist_ref/dist_algorithms.html b/doc/html/math_toolkit/dist_ref/dist_algorithms.html
index 70c9c5439..85ffa58e0 100644
--- a/doc/html/math_toolkit/dist_ref/dist_algorithms.html
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diff --git a/doc/html/math_toolkit/dist_ref/dists.html b/doc/html/math_toolkit/dist_ref/dists.html
index 97f8c0038..19f1293c0 100644
--- a/doc/html/math_toolkit/dist_ref/dists.html
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diff --git a/doc/html/math_toolkit/dist_ref/dists/arcine_dist.html b/doc/html/math_toolkit/dist_ref/dists/arcine_dist.html
index 1b1164258..e9e5ac39e 100644
--- a/doc/html/math_toolkit/dist_ref/dists/arcine_dist.html
+++ b/doc/html/math_toolkit/dist_ref/dists/arcine_dist.html
@@ -4,10 +4,11 @@
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diff --git a/doc/html/math_toolkit/dist_ref/dists/bernoulli_dist.html b/doc/html/math_toolkit/dist_ref/dists/bernoulli_dist.html
index 463924e7b..bc96ba061 100644
--- a/doc/html/math_toolkit/dist_ref/dists/bernoulli_dist.html
+++ b/doc/html/math_toolkit/dist_ref/dists/bernoulli_dist.html
@@ -4,10 +4,11 @@
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diff --git a/doc/html/math_toolkit/dist_ref/dists/beta_dist.html b/doc/html/math_toolkit/dist_ref/dists/beta_dist.html
index b1318a5c0..070ab2dfe 100644
--- a/doc/html/math_toolkit/dist_ref/dists/beta_dist.html
+++ b/doc/html/math_toolkit/dist_ref/dists/beta_dist.html
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diff --git a/doc/html/math_toolkit/dist_ref/dists/binomial_dist.html b/doc/html/math_toolkit/dist_ref/dists/binomial_dist.html
index 7e4ee2687..ecb7a346b 100644
--- a/doc/html/math_toolkit/dist_ref/dists/binomial_dist.html
+++ b/doc/html/math_toolkit/dist_ref/dists/binomial_dist.html
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diff --git a/doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html b/doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html
index 0ca26933c..a34aacd90 100644
--- a/doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html
+++ b/doc/html/math_toolkit/dist_ref/dists/cauchy_dist.html
@@ -4,10 +4,11 @@