Moments of coverage of a random ellipsoid (Q1073500)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Moments of coverage of a random ellipsoid |
scientific article; zbMATH DE number 3945099
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Moments of coverage of a random ellipsoid |
scientific article; zbMATH DE number 3945099 |
Statements
Moments of coverage of a random ellipsoid (English)
0 references
1986
0 references
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.
0 references
content at confidence level
0 references
normal distribution
0 references
moments of coverage
0 references
random ellipsoid
0 references
approximations
0 references
distribution of coverage
0 references
tolerance regions
0 references
quadratic form in normal variables
0 references
