A nonparametric control chart based on a bivariate signed-rank test is developed for monitoring the changes in the location of a bivariate process. The average run length performance of the proposed nonparametric chart is investigated using a simulation study and is compared with a parametric control chart under bivariate normal and bivariate double exponential distributions. Further the perfor...

By using well known properties of elliptical distributions we show that the relation between Kendall's tau and the linear correlation coefficient for bivariate normal distributions holds more generally (subject to only slight modifications) for the class of elliptical distributions.

This paper deals with the arithmetization of univariate and bivariate distributions, i.e. with their transformation into discrete distributions defined on the non-negative integers. Numerical aspects are investigated.

Four robust estimators of multivariate locations are compared in a Monte Carlo study by examining their empirical efficiency performance on a range of bivariate distributions with heavier tails than the Gaussian distribution. Using three different multivariate measures of relative efficiency, the simulation results show that the Hodges-Lehmann estimator is "safest" among the robust estimators, ...

We derive the distributions of W = X/(X +Y ) (equivalently, X/Y ) and P = XY and the the corresponding moment properties when X and Y follow Arnold and Strauss’s bivariate exponential distribution. The expressions turn out to involve several special functions. We also provide extensive tabulations of the percentage points associated with the two distributions. These tables – obtained using inte...