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The Probability Content of Cones in Isotropic Random Fields

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  • Provost, Serge B.
  • Cheong, Young-Ho
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    Abstract

    This paper provides computable representations for the evaluation of the probability content of cones in isotropic random fields. A decomposition of quadratic forms in spherically symmetric random vectors is obtained and a representation of their moments is derived in terms of finite sums. These results are combined to obtain the distribution function of quadratic forms in spherically symmetric or central elliptically contoured random vectors. Some numerical examples involving the sample serial covariance are provided. Ratios of quadratic forms are also discussed.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 66 (1998)
    Issue (Month): 2 (August)
    Pages: 237-254

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    Handle: RePEc:eee:jmvana:v:66:y:1998:i:2:p:237-254

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    Related research

    Keywords: Spherically symmetric distributions elliptically contoured distributions quadratic forms cones exact distribution moments serial covariance;

    References

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    1. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
    2. Osiewalski, J. & Steel, M.F.J., 1990. "Robust Bayesian inference in elliptical regression models," Discussion Paper 1990-32, Tilburg University, Center for Economic Research.
    3. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
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