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Moments of coverage of a random ellipsoid

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Summary

Exact expressions are obtained for the moments of coverage of the random ellipsoid

$$T_r (\bar x,S(X)) = \{ y|(y - \bar x)'S^{ - 1} (X)(y - \bar x) \leqq r\}$$

whereX=p1,...,p n is a sample from aN p (μ, Σ) distribution. This leads to approximations for the distribution of coverage and a solution to a problem in tolerance regions. An alternative expression is obtained for the distribution function of a quadratic form in normal variables.

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Authors and Affiliations

  1. University of Toronto, Toronto, Canada

    Michael Evans

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  1. Michael Evans
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Evans, M. Moments of coverage of a random ellipsoid. Ann Inst Stat Math 38, 23–33 (1986). https://doi.org/10.1007/BF02482497

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  • DOI: https://doi.org/10.1007/BF02482497

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