 |
BUILT-IN MATHEMATICA SYMBOL
KendallTau
KendallTau[v1, v2]
gives Kendall's rank correlation coefficient 
for the vectors 
and 
.
KendallTau[m]
gives Kendall's rank correlation coefficients 
for the matrix m.
KendallTau[m1, m2]
gives Kendall's rank correlation coefficients 
for the matrices 
and 
.
KendallTau[dist]
gives Kendall's rank correlation matrix for the multivariate symbolic distribution dist.
KendallTau[dist, i, j]
gives the 
Kendall rank correlation for the multivariate symbolic distribution dist.
Details
- KendallTau[v1, v2] gives Kendall's rank correlation coefficient
between 
and 
. - Kendall's
is a measure of monotonic association based on the relative order of consecutive elements in the two lists. - Kendall's
between 
and 
is given by 
, where 
is the number of concordant pairs of observations, 
is the number of discordant pairs, 
is the number of ties involving only the 
variable, and 
is the number of ties involving only the 
variable. - 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 
. - The tie-corrected version of Kendall's
returned is sometimes referred to as Kendall's Tau-b. - The arguments
and 
can be any real-valued vectors of equal length. - For a matrix m with
columns, KendallTau[m] is a 
×
matrix of the rank-correlations between columns of m. - For an
×
matrix 
and an 
×
matrix 
, KendallTau[m1, m2] is a 
×
matrix of the rank-correlations between columns of 
and columns of 
. - KendallTau[dist, i, j] is the probability of concordance minus the probability of discordance Probability[(x1-x2)(y1-y2)>0, {{x1, y1}
disti, j, {x2, y2}disti, j}]-Probability[(x1-x2)(y1-y2)<0, {{x1, y1}disti, j, {x2, y2}disti, j}] where 
is the 
marginal of dist. - KendallTau[dist] gives a matrix
where the 
entry is given by KendallTau[dist, i, j].
New in 9
