BlomqvistBeta

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

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

BlomqvistBeta[m1, m2]
gives Blomqvist's medial correlation coefficient 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 between and .
  • Blomqvist's between vectors x and y is given by Correlation[Sign[x-x], Sign[y-y]], where and are the medians of x and y, respectively.
  • The arguments and can be any real-valued vectors of equal length.
  • For a matrix m with columns BlomqvistBeta[m] is a × matrix of the 's between columns of m.
  • For an × matrix and an × matrix BlomqvistBeta[m1, m2] is a × matrix of the 's between columns of and columns of .
  • BlomqvistBeta[dist, i, j] is Probability[(x-x)(y-y)>0, {x, y}Distributeddisti, j]-Probability[(x-x)(y-y)<0, {x, y}Distributeddisti, 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 where the ^(th) entry is given by BlomqvistBeta[dist, i, j].

ExamplesExamplesopen allclose all

Basic Examples (4)Basic Examples (4)

Blomqvist's for two vectors:

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Blomqvist's for a matrix:

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Blomqvist's for two matrices:

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Compute Blomqvist's matrix for a bivariate distribution:

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Compare to a simulated value:

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