An efficient method for generating a uniform distribution of points within a hypersphere

This work demonstrates the analytical equivalence of two ostensibly different, efficient methods [M. Sibuya, Ann. Inst. Stat. Math. 14, 81 (1964); Y. Tashiro, Ann. Inst. Stat. Math. A 29, 295 (1977); G. Marsaglia, J. Stat. Comput. Simul. 11, 71 (1980)] for generating a uniform distribution of points within a hypersphere of arbitrary integer dimensionality D. A modified version of these methods is provided that appears to be computationally superior. One useful application of the present method is the efficient evaluation of a class of high‐dimensional integrals.