diff --git a/doc/html/backgrounders.html b/doc/html/backgrounders.html index 86ab4b66b3..b29bcfd47e 100644 --- a/doc/html/backgrounders.html +++ b/doc/html/backgrounders.html @@ -4,11 +4,10 @@ Chapter 23. Backgrounders - - + + - @@ -51,7 +50,9 @@ -
+ + +
+

PrevUpHomeNext diff --git a/doc/html/constants.html b/doc/html/constants.html index 6ebbbe5ad3..d606b0db59 100644 --- a/doc/html/constants.html +++ b/doc/html/constants.html @@ -4,11 +4,10 @@ Chapter 4. Mathematical Constants - - + + - @@ -44,7 +43,9 @@ -
+ + +
+

PrevUpHomeNext diff --git a/doc/html/cstdfloat.html b/doc/html/cstdfloat.html index bd34f49604..bf38d84cff 100644 --- a/doc/html/cstdfloat.html +++ b/doc/html/cstdfloat.html @@ -4,11 +4,10 @@ Chapter 3. Specified-width floating-point typedefs - - + + - @@ -52,7 +51,9 @@ -
+ + +
+

PrevUpHomeNext diff --git a/doc/html/dist.html b/doc/html/dist.html index a0c6c30929..204ba06791 100644 --- a/doc/html/dist.html +++ b/doc/html/dist.html @@ -4,11 +4,10 @@ Chapter 5. Statistical Distributions and Functions - - + + - @@ -207,7 +206,9 @@ -
+ + +
+

PrevUpHomeNext diff --git a/doc/html/extern_c.html b/doc/html/extern_c.html index 27485f538a..9a01395650 100644 --- a/doc/html/extern_c.html +++ b/doc/html/extern_c.html @@ -4,11 +4,10 @@ Chapter 9. TR1 and C99 external "C" Functions - - + + - @@ -35,7 +34,9 @@ -
+ + +
+

PrevUpHomeNext diff --git a/doc/html/filters.html b/doc/html/filters.html index e66f217193..332d9b21e7 100644 --- a/doc/html/filters.html +++ b/doc/html/filters.html @@ -4,11 +4,10 @@ Chapter 14. Filters - - + + - @@ -31,7 +30,9 @@
Daubechies Filters
-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/gcd_lcm.html b/doc/html/gcd_lcm.html index 083588afd2..a656eb9b57 100644 --- a/doc/html/gcd_lcm.html +++ b/doc/html/gcd_lcm.html @@ -4,11 +4,10 @@ Chapter 18. Integer Utilities (Greatest Common Divisor and Least Common Multiple) - - + + - @@ -36,7 +35,9 @@ continue to exist and redirect to the moved headers.

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/index.html b/doc/html/index.html index ebf1df493e..b5ebdf6e15 100644 --- a/doc/html/index.html +++ b/doc/html/index.html @@ -1,12 +1,11 @@ -Math Toolkit 4.1.1 +Math Toolkit 4.1.0 - + - @@ -23,7 +22,7 @@

-Math Toolkit 4.1.1

+Math Toolkit 4.1.0

Nikhar Agrawal @@ -134,7 +133,10 @@

- +
+ + +

Last revised: February 23, 2023 at 18:11:17 GMT


Next
diff --git a/doc/html/indexes.html b/doc/html/indexes.html index 2b99eff987..f3d1541533 100644 --- a/doc/html/indexes.html +++ b/doc/html/indexes.html @@ -4,11 +4,10 @@ Chapter 25. Indexes - - + + - @@ -37,7 +36,9 @@ -
+ + +
+

PrevUpHomeNext diff --git a/doc/html/indexes/s01.html b/doc/html/indexes/s01.html index bdd7521830..2b5d2dfe85 100644 --- a/doc/html/indexes/s01.html +++ b/doc/html/indexes/s01.html @@ -4,11 +4,10 @@ Function Index - + - @@ -25,7 +24,7 @@

-Function Index

+Function Index

1 2 4 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/indexes/s02.html b/doc/html/indexes/s02.html index db175c17e5..4850bc7c7c 100644 --- a/doc/html/indexes/s02.html +++ b/doc/html/indexes/s02.html @@ -4,11 +4,10 @@ Class Index - + - @@ -25,7 +24,7 @@

-Class Index

+Class Index

A B C D E F G H I K L M N O P Q R S T U V W

@@ -467,7 +466,9 @@
-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/indexes/s03.html b/doc/html/indexes/s03.html index 2c28b94101..2b8a2b5b62 100644 --- a/doc/html/indexes/s03.html +++ b/doc/html/indexes/s03.html @@ -4,11 +4,10 @@ Typedef Index - + - @@ -25,7 +24,7 @@

-Typedef Index

+Typedef Index

A B C D E F G H I K L N P R S T U V W

@@ -386,7 +385,9 @@
-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/indexes/s04.html b/doc/html/indexes/s04.html index e6748a3007..644a774352 100644 --- a/doc/html/indexes/s04.html +++ b/doc/html/indexes/s04.html @@ -4,11 +4,10 @@ Macro Index - + - @@ -25,7 +24,7 @@

-Macro Index

+Macro Index

B F

@@ -374,7 +373,9 @@
-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/indexes/s05.html b/doc/html/indexes/s05.html index ba5052d7f8..1d13dcd6bb 100644 --- a/doc/html/indexes/s05.html +++ b/doc/html/indexes/s05.html @@ -4,10 +4,9 @@ Index - + - @@ -24,7 +23,7 @@

-Index

+Index

1 2 4 5 7 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z _

-
+ + +
+

PrevUpHome diff --git a/doc/html/internals.html b/doc/html/internals.html index 56aa0eccc4..daf0ab7b2c 100644 --- a/doc/html/internals.html +++ b/doc/html/internals.html @@ -4,11 +4,10 @@ Chapter 19. Internal Details: Series, Rationals and Continued Fractions, Testing, and Development Tools - - + + - @@ -57,7 +56,9 @@ -
+ + +
+

PrevUpHomeNext diff --git a/doc/html/interpolation.html b/doc/html/interpolation.html index b603e18533..2d54f46114 100644 --- a/doc/html/interpolation.html +++ b/doc/html/interpolation.html @@ -4,11 +4,10 @@ Chapter 12. Interpolation - - + + - @@ -51,7 +50,9 @@ -
+ + +
+

PrevUpHomeNext diff --git a/doc/html/inverse_complex.html b/doc/html/inverse_complex.html index ffffbc7595..781eea65cd 100644 --- a/doc/html/inverse_complex.html +++ b/doc/html/inverse_complex.html @@ -4,11 +4,10 @@ Chapter 15. Complex Number Functions - - + + - @@ -47,7 +46,9 @@ Report on C++ Library Extensions.

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/acknowledgement.html b/doc/html/math_toolkit/acknowledgement.html index 32ec4dd3ee..52eaee594f 100644 --- a/doc/html/math_toolkit/acknowledgement.html +++ b/doc/html/math_toolkit/acknowledgement.html @@ -4,11 +4,10 @@ Acknowledgements - + - @@ -34,7 +33,9 @@ section. Thank you to all who contributed to the discution about this library.

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/acknowledgements.html b/doc/html/math_toolkit/acknowledgements.html index 15d6762589..0a0906b9d4 100644 --- a/doc/html/math_toolkit/acknowledgements.html +++ b/doc/html/math_toolkit/acknowledgements.html @@ -4,11 +4,10 @@ Acknowledgements - + - @@ -34,7 +33,9 @@ section. Thank you to all who contributed to the discussion about this library.

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/acos.html b/doc/html/math_toolkit/acos.html index dc9e90dc63..f813c0b1d2 100644 --- a/doc/html/math_toolkit/acos.html +++ b/doc/html/math_toolkit/acos.html @@ -4,11 +4,10 @@ acos - + - @@ -48,7 +47,9 @@
Formula:

-
+ + +
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/acosh.html b/doc/html/math_toolkit/acosh.html index f137666eae..a0130c330f 100644 --- a/doc/html/math_toolkit/acosh.html +++ b/doc/html/math_toolkit/acosh.html @@ -4,11 +4,10 @@ acosh - + - @@ -48,7 +47,9 @@
Formula:

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+ + +
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/airy.html b/doc/html/math_toolkit/airy.html index f278a7397e..272a42631a 100644 --- a/doc/html/math_toolkit/airy.html +++ b/doc/html/math_toolkit/airy.html @@ -4,11 +4,10 @@ Airy Functions - + - @@ -35,7 +34,9 @@
Finding Zeros of Airy Functions
-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/airy/ai.html b/doc/html/math_toolkit/airy/ai.html index 2aa4357847..bc4cde1534 100644 --- a/doc/html/math_toolkit/airy/ai.html +++ b/doc/html/math_toolkit/airy/ai.html @@ -4,11 +4,10 @@ Airy Ai Function - + - @@ -116,7 +115,9 @@

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/airy/aip.html b/doc/html/math_toolkit/airy/aip.html index 13621f8ca0..a16bc4113c 100644 --- a/doc/html/math_toolkit/airy/aip.html +++ b/doc/html/math_toolkit/airy/aip.html @@ -4,11 +4,10 @@ Airy Ai' Function - + - @@ -108,7 +107,9 @@

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/airy/airy_root.html b/doc/html/math_toolkit/airy/airy_root.html index 43bfee0eef..4f5dcfdbc8 100644 --- a/doc/html/math_toolkit/airy/airy_root.html +++ b/doc/html/math_toolkit/airy/airy_root.html @@ -4,11 +4,10 @@ Finding Zeros of Airy Functions - + - @@ -461,7 +460,9 @@

Alpha.

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/airy/bi.html b/doc/html/math_toolkit/airy/bi.html index 78e19f5846..14b6541e97 100644 --- a/doc/html/math_toolkit/airy/bi.html +++ b/doc/html/math_toolkit/airy/bi.html @@ -4,11 +4,10 @@ Airy Bi Function - + - @@ -107,7 +106,9 @@

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/airy/bip.html b/doc/html/math_toolkit/airy/bip.html index 411b622fba..77ac68c130 100644 --- a/doc/html/math_toolkit/airy/bip.html +++ b/doc/html/math_toolkit/airy/bip.html @@ -4,11 +4,10 @@ Airy Bi' Function - + - @@ -108,7 +107,9 @@

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/anderson_darling.html b/doc/html/math_toolkit/anderson_darling.html index 6ee8655a78..f9a66831ea 100644 --- a/doc/html/math_toolkit/anderson_darling.html +++ b/doc/html/math_toolkit/anderson_darling.html @@ -4,11 +4,10 @@ The Anderson-Darling Test - + - @@ -191,7 +190,9 @@

of the Anderson-Darling test statistic agrees with Mathematica.

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/archetypes.html b/doc/html/math_toolkit/archetypes.html index 01a0539917..6b8083aab2 100644 --- a/doc/html/math_toolkit/archetypes.html +++ b/doc/html/math_toolkit/archetypes.html @@ -4,11 +4,10 @@ Conceptual Archetypes for Reals and Distributions - + - @@ -178,7 +177,9 @@

implemented in there too.)

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/asin.html b/doc/html/math_toolkit/asin.html index d24d241600..f41968c9ff 100644 --- a/doc/html/math_toolkit/asin.html +++ b/doc/html/math_toolkit/asin.html @@ -4,11 +4,10 @@ asin - + - @@ -48,7 +47,9 @@
Formula:

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/asinh.html b/doc/html/math_toolkit/asinh.html index 42166c69b9..f495ad9a46 100644 --- a/doc/html/math_toolkit/asinh.html +++ b/doc/html/math_toolkit/asinh.html @@ -4,11 +4,10 @@ asinh - + - @@ -48,7 +47,9 @@
Formula:

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/atan.html b/doc/html/math_toolkit/atan.html index 6ebf1f0a3f..6189591fee 100644 --- a/doc/html/math_toolkit/atan.html +++ b/doc/html/math_toolkit/atan.html @@ -4,11 +4,10 @@ atan - + - @@ -48,7 +47,9 @@
Formula:

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/atanh.html b/doc/html/math_toolkit/atanh.html index 4e63a8612b..16e89c8fb4 100644 --- a/doc/html/math_toolkit/atanh.html +++ b/doc/html/math_toolkit/atanh.html @@ -4,11 +4,10 @@ atanh - + - @@ -48,7 +47,9 @@
Formula:

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/autodiff.html b/doc/html/math_toolkit/autodiff.html index fd4fdc5876..6e4b20a98b 100644 --- a/doc/html/math_toolkit/autodiff.html +++ b/doc/html/math_toolkit/autodiff.html @@ -4,11 +4,10 @@ Automatic Differentiation - + - @@ -400,7 +399,9 @@

manual.

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bad_guess.html b/doc/html/math_toolkit/bad_guess.html index d873721a2f..756d317647 100644 --- a/doc/html/math_toolkit/bad_guess.html +++ b/doc/html/math_toolkit/bad_guess.html @@ -4,11 +4,10 @@ The Effect of a Poor Initial Guess - + - @@ -758,7 +757,9 @@ when using derivatives.

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bad_roots.html b/doc/html/math_toolkit/bad_roots.html index df4e4eccc9..f26e434e0d 100644 --- a/doc/html/math_toolkit/bad_roots.html +++ b/doc/html/math_toolkit/bad_roots.html @@ -4,11 +4,10 @@ Examples Where Root Finding Goes Wrong - + - @@ -109,7 +108,9 @@

and for z0 > 0 the steps are actually divergent.

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/barycentric.html b/doc/html/math_toolkit/barycentric.html index 5d443533af..659ded546f 100644 --- a/doc/html/math_toolkit/barycentric.html +++ b/doc/html/math_toolkit/barycentric.html @@ -4,11 +4,10 @@ Barycentric Rational Interpolation - + - @@ -269,7 +268,9 @@

Root was found in 10 iterations. -

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bessel.html b/doc/html/math_toolkit/bessel.html index ba429d56ec..bfcd26d3b7 100644 --- a/doc/html/math_toolkit/bessel.html +++ b/doc/html/math_toolkit/bessel.html @@ -4,11 +4,10 @@ Bessel Functions - + - @@ -41,7 +40,9 @@ the Bessel Functions -
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bessel/bessel_derivatives.html b/doc/html/math_toolkit/bessel/bessel_derivatives.html index 9c3b68f06c..129a03766d 100644 --- a/doc/html/math_toolkit/bessel/bessel_derivatives.html +++ b/doc/html/math_toolkit/bessel/bessel_derivatives.html @@ -4,11 +4,10 @@ Derivatives of the Bessel Functions - + - @@ -1437,7 +1436,9 @@

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bessel/bessel_first.html b/doc/html/math_toolkit/bessel/bessel_first.html index 46e55e05d8..e5942506b6 100644 --- a/doc/html/math_toolkit/bessel/bessel_first.html +++ b/doc/html/math_toolkit/bessel/bessel_first.html @@ -4,11 +4,10 @@ Bessel Functions of the First and Second Kinds - + - @@ -1368,7 +1367,9 @@
recurrence.

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bessel/bessel_over.html b/doc/html/math_toolkit/bessel/bessel_over.html index 1960c93cec..c2a200ddf3 100644 --- a/doc/html/math_toolkit/bessel/bessel_over.html +++ b/doc/html/math_toolkit/bessel/bessel_over.html @@ -4,11 +4,10 @@ Bessel Function Overview - + - @@ -216,7 +215,9 @@
and sph_neumann.

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PrevUpHomeNext diff --git a/doc/html/math_toolkit/bessel/bessel_root.html b/doc/html/math_toolkit/bessel/bessel_root.html index 92971a0641..f2d03c3a7a 100644 --- a/doc/html/math_toolkit/bessel/bessel_root.html +++ b/doc/html/math_toolkit/bessel/bessel_root.html @@ -4,11 +4,10 @@ Finding Zeros of Bessel Functions of the First and Second Kinds - + - @@ -756,7 +755,9 @@

Alpha.

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bessel/mbessel.html b/doc/html/math_toolkit/bessel/mbessel.html index bfd73b84d5..1d5880d21b 100644 --- a/doc/html/math_toolkit/bessel/mbessel.html +++ b/doc/html/math_toolkit/bessel/mbessel.html @@ -4,11 +4,10 @@ Modified Bessel Functions of the First and Second Kinds - + - @@ -1181,7 +1180,9 @@
two values and fν, the Wronskian yields Iν(x) directly.

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bessel/sph_bessel.html b/doc/html/math_toolkit/bessel/sph_bessel.html index d42a7bbfe7..025b803cc7 100644 --- a/doc/html/math_toolkit/bessel/sph_bessel.html +++ b/doc/html/math_toolkit/bessel/sph_bessel.html @@ -4,11 +4,10 @@ Spherical Bessel Functions of the First and Second Kinds - + - @@ -273,7 +272,9 @@
main definition as x → 0.

-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bezier_polynomial.html b/doc/html/math_toolkit/bezier_polynomial.html index 6dd232725e..5ec26eeeb6 100644 --- a/doc/html/math_toolkit/bezier_polynomial.html +++ b/doc/html/math_toolkit/bezier_polynomial.html @@ -4,11 +4,10 @@ Bezier Polynomials - + - @@ -234,7 +233,9 @@

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bilinear_uniform.html b/doc/html/math_toolkit/bilinear_uniform.html index e5b9a43fd4..26cca6dff2 100644 --- a/doc/html/math_toolkit/bilinear_uniform.html +++ b/doc/html/math_toolkit/bilinear_uniform.html @@ -4,11 +4,10 @@ Bilinear Uniform Interpolation - + - @@ -125,7 +124,9 @@

Bilinear<double>/8192 13.2 ns -

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/bivariate_statistics.html b/doc/html/math_toolkit/bivariate_statistics.html index 5b39e5da55..1435f61652 100644 --- a/doc/html/math_toolkit/bivariate_statistics.html +++ b/doc/html/math_toolkit/bivariate_statistics.html @@ -4,11 +4,10 @@ Bivariate Statistics - + - @@ -138,7 +137,9 @@

-

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/brent_minima.html b/doc/html/math_toolkit/brent_minima.html index 4315a77e37..de2304809a 100644 --- a/doc/html/math_toolkit/brent_minima.html +++ b/doc/html/math_toolkit/brent_minima.html @@ -4,11 +4,10 @@ Locating Function Minima using Brent's algorithm - + - @@ -650,7 +649,9 @@
-
+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/building.html b/doc/html/math_toolkit/building.html index f49a9f9e34..c270a5a7d0 100644 --- a/doc/html/math_toolkit/building.html +++ b/doc/html/math_toolkit/building.html @@ -4,11 +4,10 @@ If and How to Build a Boost.Math Library, and its Examples and Tests - + - @@ -146,7 +145,9 @@
the sources. Boost.Build will do this automatically when appropriate.

-
+ + +
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PrevUpHomeNext diff --git a/doc/html/math_toolkit/c99.html b/doc/html/math_toolkit/c99.html index 3867e13765..5881569324 100644 --- a/doc/html/math_toolkit/c99.html +++ b/doc/html/math_toolkit/c99.html @@ -4,11 +4,10 @@ C99 C Functions - + - @@ -462,7 +461,9 @@
ISO Standard

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+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/cardinal_cubic_b.html b/doc/html/math_toolkit/cardinal_cubic_b.html index faf45cf96b..62dca00371 100644 --- a/doc/html/math_toolkit/cardinal_cubic_b.html +++ b/doc/html/math_toolkit/cardinal_cubic_b.html @@ -4,11 +4,10 @@ Cardinal Cubic B-spline interpolation - + - @@ -312,7 +311,9 @@

Found in 3 iterations -

+ + +
+

PrevUpHomeNext diff --git a/doc/html/math_toolkit/cardinal_quadratic_b.html b/doc/html/math_toolkit/cardinal_quadratic_b.html index fed84661ef..adf1717940 100644 --- a/doc/html/math_toolkit/cardinal_quadratic_b.html +++ b/doc/html/math_toolkit/cardinal_quadratic_b.html @@ -4,11 +4,10 @@ Cardinal Quadratic B-spline interpolation - + - @@ -84,7 +83,9 @@

differentiable, but not three or four times differentiable.

-

+ + +
+

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of data by spline functions. Diss. City, University of London, 1975.

-

+ + +
+

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-

+ + +
+

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-

+ + +
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} // Namespaces -

+ + +
+

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Boost C++ LibrariesHomeLibrariesPeopleFAQMore
-
-
-PrevUpHomeNext -
-
- -

- - Synopsis -

-
#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);
-}
-
-

- - Description -

-

- 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. -

-

- - Invariants -

-

- 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. -

-

- - References -

-
  • - Chatterjee, Sourav. "A new coefficient of correlation." Journal - of the American Statistical Association 116.536 (2021): 2009-2022. -
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