Distributions on spheres and random variables distributed on the interval (−1,1)

✍ Scribed by James R. Schott

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 187 KB
• Volume: 62
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(03)00043-9

✦ Synopsis

In this paper, we look at a simple relationship between a random vector having a continuous distribution on the unit m-sphere and m random variables, m -1 of which have a distribution on the interval (-1; 1), while the ÿnal random variable is a discrete one taking on the values -1 and 1. This relationship can be particularly useful when these m random variables are independently distributed. In this case, it can be used to construct distributions on the unit m-sphere having speciÿc features as well as to generate random vectors having these distributions.