# BlomqvistBeta

BlomqvistBeta[v1,v2]

gives Blomqvist's medial correlation coefficient β for the vectors v1 and v2.

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

BlomqvistBeta[m1,m2]

gives Blomqvist's medial correlation coefficient β for the matrices m1 and m2.

BlomqvistBeta[dist]

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

BlomqvistBeta[dist,i,j]

gives the (i,j) medial correlation coefficient for the multivariate symbolic distribution dist.

# Details • BlomqvistBeta[v1,v2] gives Blomqvist's medial correlation coefficient β between v1 and v2.
• Blomqvist's β between vectors x and y is given by Correlation[Sign[x-μx],Sign[y-μy]], where μx and μy are the medians of x and y, respectively.
• The arguments v1 and v2 can be any realvalued vectors of equal length.
• For a matrix m with columns is a × matrix of the β's between columns of m.
• For an × matrix m1 and an × matrix m2 BlomqvistBeta[m1,m2] is a × matrix of the β's between columns of m1 and columns of m2.
• 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 disti,j is the  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  entry is given by BlomqvistBeta[dist,i,j].

# Examples

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## Basic Examples(4)

Blomqvist's β for two vectors:

 In:= In:= Out= Blomqvist's β for a matrix:

 In:= In:= Out//MatrixForm= Blomqvist's β for two matrices:

 In:= In:= In:= Out//MatrixForm= Compute Blomqvist's β matrix for a bivariate distribution:

 In:= In:= Out//MatrixForm= Compare to a simulated value:

 In:= Out//MatrixForm= ## Properties & Relations(7)

Introduced in 2012
(9.0)