Simulation and Visualization of 3D-Spherical Distributions

In this paper, we consider simulation and visualization of spherical distributions as well as plotting of densities and histograms on the sphere, in support of the dictum, “A picture is worth a thousand words.” This is in many ways a companion paper to the recently published theoretical article by the authors on spherical harmonics (Jammalamadaka and Terdik in J Multivariate Anal 171:436–451, 2019 [1]). We provide computational algorithms to simulate several of the spherical models discussed there and provide alternate and improved methods in some cases. This allows a user to choose between alternate approaches for generating such random variates, and in depicting them via plots and histograms. The algorithms are made available in a MATLAB package titled “3D-Directional Statistics, Simulation, and Visualization” abbreviated 3D-Directional-SSV which is available at MATLAB, File Exchange, and also posted on GitHub. This work is especially appropriate in this volume celebrating Florence Nightingale, the progenitor of what we now call the rose diagram in two dimensions.