Moments of coverage of a random ellipsoid (Q1073500)

Exact expressions are obtained for the moments of coverage of the random ellipsoid \[ T_ r(\bar x,S(X))=\{y| (y-\bar x)'S^{-1}(X)(y-\bar x)\leq r\}, \] where \(X=(x_ 1,...,x_ n)\) is a sample from a \(N_ p(\mu,\Sigma)\) 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.