Clockwise Bivariate Boxplots

In this paper we suggest a simple way of constructing a robust non parametric bivariate contour based on the rotation of the univariate box-plot which does not necessarily have to use a bivariate generalization of the univariate depth measures. The suggested approach is based on the projection of bivariate data along the round angle. When the angle is a multiple of π/2 we obtain the traditional univariate boxplot referred to each variable. In all the other cases we obtain univariate boxplots which keep into account in a different way the correlation between the two original variables. We apply the suggested approach to some datasets and exploit the properties of the different choices of defining the inner region and the outer contour. The final result is a simple and easy to construct bivariate boxplot which enables to visualize the location, spread skewness and tails of the data.