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

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  • Schott, James R.

Abstract

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 final 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 specific features as well as to generate random vectors having these distributions.

Suggested Citation

  • Schott, James R., 2003. "Distributions on spheres and random variables distributed on the interval (-1,1)," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 391-396, May.
    • Handle: RePEc:eee:stapro:v:62:y:2003:i:4:p:391-396
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    References listed on IDEAS

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    1. Saw, John G., 1984. "Ultraspherical polynomials and statistics on the m-sphere," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 105-113, February.
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