Title: Boxplots for directional data
Authors: Giovanni Camillo Porzio - University of Cassino and Southern Lazio (Italy) [presenting]
Davide Buttarazzi - University of Cassino and Southern Lazio (Italy)
Giuseppe Pandolfo - University of Naples Federico II (Italy)
Christophe Ley - Ghent University (Belgium)
Abstract: Tukey's box-and-whiskers plot is probably one of the most powerful ways to visually provide information on location, variability and symmetries of a univariate distribution. Accordingly, the recently introduced boxplot for circular data will be presented, along to its extension to spherical data. In analogy with the bagplot available for the Euclidean case, a spherical boxplot will be defined. It will be made up of four components: the spherical median, the spherical convex hull of the 50\% deepest observations on a sphere (i.e., the box), the spherical convex hull of the remaining points lying within the fences (i.e., the whiskers), the set of far out values (i.e., the potential outliers), if any. The methods will be illustrated through both simulated and real data sets.