GoodmanKruskalGamma

GoodmanKruskalGamma[v1,v2]
gives the GoodmanKruskal coefficient for the vectors and .

GoodmanKruskalGamma[m]
gives the GoodmanKruskal coefficients for the matrix m.

GoodmanKruskalGamma[m1,m2]
gives the GoodmanKruskal coefficients for the matrices and .

GoodmanKruskalGamma[dist]
gives the coefficient matrix for the multivariate symbolic distribution dist.

GoodmanKruskalGamma[dist,i,j]
gives the ^(th) coefficient for the multivariate symbolic distribution dist.

DetailsDetails

  • GoodmanKruskalGamma[v1,v2] gives the GoodmanKruskal coefficient between and .
  • GoodmanKruskal is a measure of monotonic association based on the relative order of consecutive elements in the two lists.
  • GoodmanKruskal between and is given by , where is the number of concordant pairs of observations and is the number of discordant pairs.
  • A concordant pair of observations and is one such that both and or both and . A discordant pair of observations is one such that and or and .
  • If no ties are present, is equivalent to KendallTau.
  • The arguments and can be any realvalued vectors of equal length.
  • For a matrix m with columns, GoodmanKruskalGamma[m] is a × matrix of the -coefficients between columns of m.
  • For an × matrix and an × matrix , GoodmanKruskalGamma[m1,m2] is a × matrix of the -coefficients between columns of and columns of .
  • GoodmanKruskalGamma[dist,i,j] gives where is equal to Probability[(x1-x2)(y1-y2)>0,{{x1,y1}disti,j,{x2,y2}disti,j}] and is equal to Probability[(x1-x2)(y1-y2)<0,{{x1,y1}disti,j,{x2,y2}disti,j}] where is the ^(th) marginal of dist.
  • GoodmanKruskalGamma[dist] gives a matrix where the ^(th) entry is given by GoodmanKruskalGamma[dist,i,j].

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

GoodmanKruskal for two vectors:

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GoodmanKruskal for a matrix:

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GoodmanKruskal for two matrices:

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Compute the GoodmanKruskal for a bivariate distribution:

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Compare to a simulated value:

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Introduced in 2012
(9.0)