TY - DATA T1 - A new unified approach for the simulation of a wide class of directional distributions PY - 2017/10/16 AU - John T. Kent AU - Asaad M. Ganeiber AU - Kanti V. Mardia UR - https://tandf.figshare.com/articles/dataset/A_new_unified_approach_for_the_simulation_of_a_wide_class_of_directional_distributions/5503723 DO - 10.6084/m9.figshare.5503723.v1 L4 - https://ndownloader.figshare.com/files/9524338 L4 - https://ndownloader.figshare.com/files/9524341 L4 - https://ndownloader.figshare.com/files/9524344 L4 - https://ndownloader.figshare.com/files/9524347 L4 - https://ndownloader.figshare.com/files/9524350 L4 - https://ndownloader.figshare.com/files/9524353 KW - acceptance-rejection KW - angular central Gaussian distribution KW - Bingham distribution KW - bivariate von Mises sine distribution KW - matrix Fisher distribution KW - simulation efficiency N2 - The need for effective simulation methods for directional distributions has grown as they have become components in more sophisticated statistical models. A new acceptance-rejection method is proposed and investigated for the Bingham distribution on the sphere using the angular central Gaussian distribution as an envelope. It is shown that the proposed method has high efficiency and is also straightforward to use. Next, the simulation method is extended to the Fisher and Fisher-Bingham distributions on spheres and related manifolds. Together, these results provide a widely applicable and efficient methodology to simulate many of the standard models in directional data analysis. An R package simdd, available in the online supplementary material, implements these simulation methods. ER -