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Tashiro (Ann Inst Stat Math 29:295-300, 1977) studied methods for generating unform points on the surface of the regular unit sphere. The L p -norm unit sphere is a generalization of the regular unit sphere. In this paper we propose a method associated with an algorithm for generating uniformly scattered points on the L p -norm unit sphere and discuss its applications in statistical simulation, representative points of a wide class of multivariate probability distributions and optimization problems. Some examples are illustrated for these applications. © 2007 Springer-Verlag.