  A graphical tool for investigating unimodality of hyperspherical data is
proposed. It is based on the notion of statistical data depth function for
directional data which extends the univariate concept of rank. Firstly a local
version of distance-based depths for directional data based on aims at
analyzing the local structure of hyperspherical data is proposed. Then such
notion is compared to the global version of data depth by means of a
two-dimensional scatterplot, i.e. the GLD-plot. The proposal is illustrated on
simulated and real data examples.
