The simulation of spherical distributions in the Fisher-Bingham family

The problem of generating pseudo-random unit vectors from the Fisher-Bingham distribution is considered. Attention is focussed on a subfamily known as FB_6' which includes many of the spherical distributions of practical interest, including those of Dimroth-Watson, FB_4' FB₅ and Bingham type. The rejection procedures suggested here for these distributions should prove adequate for most practical purposes. Possibilities for simulating from the general Fisher-Bingham distribution are also mentioned briefly.