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The Probability Content of Cones in Isotropic Random Fields


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


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.

Suggested Citation

  • Provost, Serge B. & Cheong, Young-Ho, 1998. "The Probability Content of Cones in Isotropic Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 66(2), pages 237-254, August.
  • Handle: RePEc:eee:jmvana:v:66:y:1998:i:2:p:237-254

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    References listed on IDEAS

    1. Osiewalski, Jacek & Steel, Mark F. J., 1993. "Robust bayesian inference in elliptical regression models," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 345-363.
    2. 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.
    3. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
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