On a combination method of VDR and patchwork for generating uniform random points on a unit sphere

Zhenhai Yang, W.K. Pang, S.H. Hou and P.K. Leung

Journal of Multivariate Analysis, 2005, vol. 95, issue 1, 23-36

Abstract: In this paper, we use a combination of VDR theory and patchwork method to derive an efficient algorithm for generating uniform random points on a unit d-sphere. We first propose an algorithm to generate random vector with uniform distribution on a unit 2-sphere on the plane. Then we use VDR theory to reduce random vector Xd with uniform distribution on a unit d-sphere into , such that the random vector (Xd-1,Xd) is uniformly distributed on a unit 2-sphere and Xd-2 has conditional uniform distribution on a (d-2)-sphere of radius , given V=v with V having the p.d.f. . Finally, we arrive by induction at an algorithm for generating uniform random points on a unit d-sphere.

Keywords: Vertical; density; representation; Patchwork; method; Generation; of; uniform; distribution (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (1)

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