A conditional distribution approach to uniform sampling on spheres and balls in L<Subscript>p</Subscript> spaces

Liang and Ng (Metrika 68:83–98, <CitationRef CitationID="CR13">2008</CitationRef>) proposed a componentwise conditional distribution method for L <Subscript> p </Subscript>-uniform sampling on L <Subscript> p </Subscript>-norm n-spheres. On the basis of properties of a special family of L <Subscript> p </Subscript>-norm spherical distributions we suggest a wide class of algorithms for sampling uniformly distributed points on n-spheres and n-balls in L <Subscript> p </Subscript> spaces, generalizing the approach of Harman and Lacko (J Multivar Anal 101:2297–2304, <CitationRef CitationID="CR10">2010</CitationRef>), and including the method of Liang and Ng as a special case. We also present results of a numerical study proving that the choice of the best algorithm from the class significantly depends on the value of p. Copyright Springer-Verlag 2012