The interpoint depth for directional data

The notion of the interpoint depth is applied to spherical spaces by us-ing an appropriate angular distance function for data lying on the surfaceof the unit hypersphere. The traditional multivariate methods, indeed, arenot suitable for the analysis of directional data and this holds true also fordistance measures and related depth based methods. The interpoint depthfor directional data possesses some nice properties and can be used for highdimensional data analysis. This notion of depth is particularly useful toinvestigate local features of distribution such as multimodality and can beexploited to deal with many statistical problems. The behavior of the pro-posed depth is investigated by means of simulated data. In addition threeinteresting applications are presented.