BUILT-IN MATHEMATICA SYMBOL

# BlomqvistBeta

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

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 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 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}disti, j]-Probability[(x-x)(y-y)<0, {x, y}disti, j] where is the marginal of dist.
• BlomqvistBeta is not well defined for discrete distributions or in the presence of ties.
• BlomqvistBeta[dist] gives a matrix where the entry is given by BlomqvistBeta[dist, i, j].

## ExamplesExamplesopen allclose all

### Basic Examples (4)Basic Examples (4)

Blomqvist's for two vectors:

 Out[2]=

Blomqvist's for a matrix:

 Out[2]//MatrixForm=

Blomqvist's for two matrices:

 Out[3]//MatrixForm=

Compute Blomqvist's matrix for a bivariate distribution:

 Out[2]//MatrixForm=

Compare to a simulated value:

 Out[3]//MatrixForm=