  The Kendall plot ($\K$-plot) is a plot measuring dependence between the
components of a bivariate random variable. The $\K$-plot graphs the Kendall
distribution function against the distribution function of $VU$, where $V$ and
$U$ are independent uniform $[0,1]$ random variables. We associate $\K$-plots
with the receiver operating characteristic ($\ROC$) curve, a well-accepted
graphical tool in biostatistics for evaluating the ability of a biomarker to
discriminate between two populations. The most commonly used global index of
diagnostic accuracy of biomarkers is the area under the $\ROC$ curve ($\AUC$).
In parallel with the $\AUC$, we propose a novel strategy to measure the
association between random variables from a continuous bivariate distribution.
First, we discuss why the area under the conventional Kendall curve ($\AUK$)
cannot be used as an index of dependence. We then suggest a simple and
meaningful extension of the definition of the $\K$-plots and define an index of
dependence that is based on $\AUK$. This measure characterizes a wide range of
two-variable relationships, thereby completely detecting the underlying
dependence structure. Properties of the proposed index satisfy the mathematical
definition of a measure. Finally, simulations and real data examples illustrate
the applicability of the proposed method.
