BlomqvistBeta

BlomqvistBeta[v1,v2]
gives Blomqvist's medial correlation coefficient β for the vectors and .

BlomqvistBeta[m]
gives Blomqvist's medial correlation coefficient β for the matrix m.

BlomqvistBeta[m1,m2]
gives Blomqvist's medial correlation coefficient β for the matrices and .

BlomqvistBeta[dist]
gives the medial correlation coefficient matrix for the multivariate symbolic distribution dist.

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

DetailsDetails

  • BlomqvistBeta[v1,v2] gives Blomqvist's medial correlation coefficient β between and .
  • Blomqvist's β between vectors x and y is given by Correlation[Sign[x-μx],Sign[y-μy]], where and are the medians of x and y, respectively.
  • The arguments and can be any realvalued vectors of equal length.
  • For a matrix m with columns BlomqvistBeta[m] is a × matrix of the β's between columns of m.
  • For an × matrix and an × matrix BlomqvistBeta[m1,m2] is a × matrix of the β's between columns of and columns of .
  • BlomqvistBeta[dist,i,j] is Probability[(x-μx)(y-μy)>0,{x,y}disti,j]-Probability[(x-μx)(y-μy)<0,{x,y}disti,j] where is the ^(th) marginal of dist.
  • BlomqvistBeta is not well defined for discrete distributions or in the presence of ties.
  • BlomqvistBeta[dist] gives a matrix β where the ^(th) entry is given by BlomqvistBeta[dist,i,j].

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

Blomqvist's β for two vectors:

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Blomqvist's β for a matrix:

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Blomqvist's β for two matrices:

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Compute Blomqvist's β matrix for a bivariate distribution:

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Compare to a simulated value:

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Introduced in 2012
(9.0)