A conditional distribution approach to uniform sampling on spheres and balls in L-p spaces

作者：Lacko Vladimir^*; Harman Radoslav

来源：Metrika, 2012, 75(7): 939-951.

DOI：10.1007/s00184-011-0360-x

• L-p-norm
• n-sphere
• n-ball
• Uniform distribution
• p-generalized normal distribution
• Monte Carlo simulation
• Probabilistic robustness analysis

Liang and Ng (Metrika 68:83-98, 2008) proposed a componentwise conditional distribution method for L (p) -uniform sampling on L (p) -norm n-spheres. On the basis of properties of a special family of L (p) -norm spherical distributions we suggest a wide class of algorithms for sampling uniformly distributed points on n-spheres and n-balls in L (p) spaces, generalizing the approach of Harman and Lacko (J Multivar Anal 101:2297-2304, 2010), 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.

• 出版日期2012-10